How do I estimate 15 parameters with the least square method for a non-linear objective function MATLAB?

I want to estimate the parameters x1-x15 with the least square method in MATLAB. My objective function is:

sum((Pot-Potcap).^2)
Pot = x(14)*exp(-(t*log(x(1)*x(15) + 1))/x(15)) + x(14)*(exp(-(t*log(x(3)*x(15) + 1))/x(15)) + (x(7)*exp(-(t*log(x(2)*x(15) + 1))/x(15)))/(x(2) - x(3)) + (x(6)*x(7)*exp(-(t*log(x(1)*x(15) + 1))/x(15)))/((x(1) - x(3))*(x(2) - x(3)))) + x(14)*(exp(-(t*log(x(4)*x(15) + 1))/x(15)) + (x(8)*exp(-(t*log(x(3)*x(15) + 1))/x(15)))/(x(3) - x(4)) + (x(7)*x(8)*exp(-(t*log(x(2)*x(15) + 1))/x(15)))/((x(2) - x(4))*(x(3) - x(4))) + (x(6)*x(7)*x(8)*exp(-(t*log(x(1)*x(15) + 1))/x(15)))/((x(1) - x(4))*(x(2) - x(4))*(x(3) - x(4)))) - x(13)*(exp(-(t*log(x(4)*x(15) + 1))/x(15)) + (x(8)*exp(-(t*log(x(3)*x(15) + 1))/x(15)))/(x(4) - x(5)) + (x(7)*x(8)*exp(-(t*log(x(2)*x(15) + 1))/x(15)))/((x(3) - x(5))*(x(4) - x(5))) + (x(6)*x(7)*x(8)*exp(-(t*log(x(1)*x(15) + 1))/x(15)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5)))) - x(11)*((exp(-(t*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(3))*(x(2) - x(5)))/(x(9)*(x(3) - x(4))) + (x(6)*exp(-(t*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(5)))/(x(9)*(x(2) - x(4))*(x(3) - x(4)))) + x(14)*(exp(-(t*log(x(2)*x(15) + 1))/x(15)) + (x(6)*exp(-(t*log(x(1)*x(15) + 1))/x(15)))/(x(1) - x(2))) + x(12)*((exp(-(t*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(4))*(x(3) - x(5)))/(x(8)*x(9)) + (x(7)*exp(-(t*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(4))*(x(2) - x(5)))/(x(8)*x(9)*(x(2) - x(3))) + (x(6)*x(7)*exp(-(t*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)*(x(1) - x(3))*(x(2) - x(3)))) - x(13)*((exp(-(t*log(x(4)*x(15) + 1))/x(15))*(x(4) - x(5)))/x(9) + (x(8)*exp(-(t*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(5)))/(x(9)*(x(3) - x(4))) + (x(7)*x(8)*exp(-(t*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(5)))/(x(9)*(x(2) - x(4))*(x(3) - x(4))) + (x(6)*x(7)*x(8)*exp(-(t*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/(x(9)*(x(1) - x(4))*(x(2) - x(4))*(x(3) - x(4)))) + x(12)*((exp(-(t*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(4)))/(x(4) - x(5)) + (x(7)*exp(-(t*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(4)))/((x(3) - x(5))*(x(4) - x(5))) + (x(6)*x(7)*exp(-(t*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5)))) - x(11)*((exp(-(t*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(3))*(x(2) - x(4)))/((x(3) - x(5))*(x(4) - x(5))) + (x(6)*exp(-(t*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(4)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5)))) + x(14)*(exp(-(t*log(x(5)*x(15) + 1))/x(15)) + (x(9)*exp(-(t*log(x(4)*x(15) + 1))/x(15)))/(x(4) - x(5)) + (x(8)*x(9)*exp(-(t*log(x(3)*x(15) + 1))/x(15)))/((x(3) - x(5))*(x(4) - x(5))) + (x(7)*x(8)*x(9)*exp(-(t*log(x(2)*x(15) + 1))/x(15)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5))) + (x(6)*x(7)*x(8)*x(9)*exp(-(t*log(x(1)*x(15) + 1))/x(15)))/((x(1) - x(5))*(x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5)))) - x(13)*((exp(-(t*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(5)))/x(9) + (x(6)*exp(-(t*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/(x(9)*(x(1) - x(2)))) + x(12)*((exp(-(t*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(4))*(x(2) - x(5)))/(x(8)*x(9)) + (x(6)*exp(-(t*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)*(x(1) - x(2)))) - x(11)*((exp(-(t*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(4))*(x(2) - x(5)))/(x(8)*x(9)) + (x(6)*exp(-(t*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)*(x(2) - x(3)))) - x(11)*((exp(-(t*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(3))*(x(2) - x(4))*(x(2) - x(5)))/(x(7)*x(8)*x(9)) + (x(6)*exp(-(t*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(4))*(x(1) - x(5)))/(x(7)*x(8)*x(9)*(x(1) - x(2)))) - x(13)*((exp(-(t*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(5)))/x(9) + (x(7)*exp(-(t*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(5)))/(x(9)*(x(2) - x(3))) + (x(6)*x(7)*exp(-(t*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/(x(9)*(x(1) - x(3))*(x(2) - x(3)))) + x(12)*((exp(-(t*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(5)))/x(9) + (x(7)*exp(-(t*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(5)))/(x(9)*(x(3) - x(4))) + (x(6)*x(7)*exp(-(t*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/(x(9)*(x(2) - x(4))*(x(3) - x(4)))) - (x(13)*exp(-(t*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/x(9) + (x(12)*exp(-(t*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)) + (x(10)*exp(-(t*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(2))*(x(1) - x(3))*(x(1) - x(5)))/(x(9)*(x(2) - x(4))*(x(3) - x(4))) + (x(10)*exp(-(t*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(2))*(x(1) - x(3))*(x(1) - x(4)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5))) + (x(10)*exp(-(t*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(4))*(x(1) - x(5)))/(x(7)*x(8)*x(9)) - (x(11)*exp(-(t*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(4))*(x(1) - x(5)))/(x(7)*x(8)*x(9)) + (x(10)*exp(-(t*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(2))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)*(x(2) - x(3))) + (x(10)*exp(-(t*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(2))*(x(1) - x(3))*(x(1) - x(4))*(x(1) - x(5)))/(x(6)*x(7)*x(8)*x(9))

for the data Potcap and t from 1 to 21. I have tried using the code:

x = sym('x', [1 15], 'real')
t = [1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20;21]
x0 = [0.2;0.21;0.22;0.23;0.24;0.31;0.32;0.33;0.34;0.1;0.1;0.1;0.1;0.1;0.3]
lb = zeros(21,1)
ub = [Inf Inf Inf Inf Inf Inf Inf Inf Inf 1 1 1 1 1 Inf]
fnc = @(x) Fungsi(x,t,Potcap);
[p,fval] = fmincon(fnc,x0,[],[],[],[],lb,ub,@mycon)
function f = Fungsi(x, t, Potcap)
   f = sum(((x(14)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)) + x(14)*(exp(-(t.*log(x(3)*x(15) + 1))/x(15)) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15)))/(x(2) - x(3)) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/((x(1) - x(3))*(x(2) - x(3)))) + x(14)*(exp(-(t.*log(x(4)*x(15) + 1))/x(15)) + (x(8)*exp(-(t.*log(x(3)*x(15) + 1))/x(15)))/(x(3) - x(4)) + (x(7)*x(8)*exp(-(t.*log(x(2)*x(15) + 1))/x(15)))/((x(2) - x(4))*(x(3) - x(4))) + (x(6)*x(7)*x(8)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/((x(1) - x(4))*(x(2) - x(4))*(x(3) - x(4)))) - x(13)*(exp(-(t.*log(x(4)*x(15) + 1))/x(15)) + (x(8)*exp(-(t.*log(x(3)*x(15) + 1))/x(15)))/(x(4) - x(5)) + (x(7)*x(8)*exp(-(t.*log(x(2)*x(15) + 1))/x(15)))/((x(3) - x(5))*(x(4) - x(5))) + (x(6)*x(7)*x(8)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5)))) - x(11)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(3))*(x(2) - x(5)))/(x(9)*(x(3) - x(4))) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(5)))/(x(9)*(x(2) - x(4))*(x(3) - x(4)))) + x(14)*(exp(-(t.*log(x(2)*x(15) + 1))/x(15)) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/(x(1) - x(2))) + x(12)*((exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(4))*(x(3) - x(5)))/(x(8)*x(9)) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(4))*(x(2) - x(5)))/(x(8)*x(9)*(x(2) - x(3))) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)*(x(1) - x(3))*(x(2) - x(3)))) - x(13)*((exp(-(t.*log(x(4)*x(15) + 1))/x(15))*(x(4) - x(5)))/x(9) + (x(8)*exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(5)))/(x(9)*(x(3) - x(4))) + (x(7)*x(8)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(5)))/(x(9)*(x(2) - x(4))*(x(3) - x(4))) + (x(6)*x(7)*x(8)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/(x(9)*(x(1) - x(4))*(x(2) - x(4))*(x(3) - x(4)))) + x(12)*((exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(4)))/(x(4) - x(5)) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(4)))/((x(3) - x(5))*(x(4) - x(5))) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5)))) - x(11)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(3))*(x(2) - x(4)))/((x(3) - x(5))*(x(4) - x(5))) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(4)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5)))) + x(14)*(exp(-(t.*log(x(5)*x(15) + 1))/x(15)) + (x(9)*exp(-(t.*log(x(4)*x(15) + 1))/x(15)))/(x(4) - x(5)) + (x(8)*x(9)*exp(-(t.*log(x(3)*x(15) + 1))/x(15)))/((x(3) - x(5))*(x(4) - x(5))) + (x(7)*x(8)*x(9)*exp(-(t.*log(x(2)*x(15) + 1))/x(15)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5))) + (x(6)*x(7)*x(8)*x(9)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/((x(1) - x(5))*(x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5)))) - x(13)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(5)))/x(9) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/(x(9)*(x(1) - x(2)))) + x(12)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(4))*(x(2) - x(5)))/(x(8)*x(9)) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)*(x(1) - x(2)))) - x(11)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(4))*(x(2) - x(5)))/(x(8)*x(9)) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)*(x(2) - x(3)))) - x(11)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(3))*(x(2) - x(4))*(x(2) - x(5)))/(x(7)*x(8)*x(9)) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(4))*(x(1) - x(5)))/(x(7)*x(8)*x(9)*(x(1) - x(2)))) - x(13)*((exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(5)))/x(9) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(5)))/(x(9)*(x(2) - x(3))) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/(x(9)*(x(1) - x(3))*(x(2) - x(3)))) + x(12)*((exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(5)))/x(9) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(5)))/(x(9)*(x(3) - x(4))) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/(x(9)*(x(2) - x(4))*(x(3) - x(4)))) - (x(13)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/x(9) + (x(12)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(2))*(x(1) - x(3))*(x(1) - x(5)))/(x(9)*(x(2) - x(4))*(x(3) - x(4))) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(2))*(x(1) - x(3))*(x(1) - x(4)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5))) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(4))*(x(1) - x(5)))/(x(7)*x(8)*x(9)) - (x(11)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(4))*(x(1) - x(5)))/(x(7)*x(8)*x(9)) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(2))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)*(x(2) - x(3))) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(2))*(x(1) - x(3))*(x(1) - x(4))*(x(1) - x(5)))/(x(6)*x(7)*x(8)*x(9)))-Potcap).^2);
end
function [c,ceq] = mycon(x)
   c = []
   ceq = (x(10)+x(11)+x(12)+x(13)+x(14))==1
end

But running the code above meets an error saying "FMINCON requires all values returned by functions to be of data type double". I have tried many things to fix this error but it still persists. Any suggestions for the problem I have or alternatives to using the code above? Thanks.

[Walter Roberson]

You have 21 lb but only 15 variables.

You do not define Potcap in the above code.

sum of squared residues like you are doing should be fine, unless you might encounter complex values

[Rex Mantiri]

Yes the excess lb is usually ignored but I have fixed that part.

Potcap is imported data.

The problem is still there. Does the error give any clue as to what is wrong with my code?

[Walter Roberson]

Considering your use of

x = sym('x', [1 15], 'real')

I am going to guess that Potcap is symbolic instead of double precision.

Or perhaps Potcap is single() instead of double()

[Rex Mantiri]

Potcap = [0.986702168; 0.97272091; 0.957930961; 0.942424001; 0.926404439; 0.909375829; 0.891635315; 0.873329497; 0.854253377; 0.834442537; 0.813592045; 0.791234153; 0.768357994; 0.744306568; 0.719094568; 0.692488019; 0.66411648; 0.634292184; 0.602498593; 0.569711546; 0.534931653]

Here is Potcap if it helps.

[Rex Mantiri]

The added 'real' type was from when I ran a manual least squares and it gave 15 complex parameters. But after I changed it to real it ran for 26 hours and ended with:

Warning: Unable to find explicit solution. For options, see help.
> In sym/solve (line 317)

That's why I am currently trying to use the built-in MATLAB tools but I'm having no luck here too. Would it help if I gave the code that I used to determine the function Pot?

Answer 1

[Walter Roberson]

I am encountering an oddity. When I execute this code on my system, I do not get the "badly scaled", and I get a much better outcome. Furthermore if I restrict the number of iterations to (say) 2000 here then I get a much better outcome than what you see below.

The outcome I get on my system is

2.78592627618734

2.88871084081361

2.25105403422586

0.461395545224784

29.1302865591129

8.13171865752827

6.46299460979685

8.57614086623395

0.907578785962305

0.914773654903989

0.0722664894980859

0.00683972729472146

5.20591012847305e-05

0.00606806920191916

241.694759335038

for an fval of about 0.014.

I will follow up with Mathworks as to why I get such different answers here.

format long g
Potcap = [0.986702168; 0.97272091; 0.957930961; 0.942424001; 0.926404439; 0.909375829; 0.891635315; 0.873329497; 0.854253377; 0.834442537; 0.813592045; 0.791234153; 0.768357994; 0.744306568; 0.719094568; 0.692488019; 0.66411648; 0.634292184; 0.602498593; 0.569711546; 0.534931653];
t = [1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20;21];
x0 = [0.2;0.21;0.22;0.23;0.24;0.31;0.32;0.33;0.34;0.1;0.1;0.1;0.1;0.1;0.3];
lb = zeros(15,1);
ub = [Inf Inf Inf Inf Inf Inf Inf Inf Inf 1 1 1 1 1 Inf];
fnc = @(x) Fungsi(x,t,Potcap);

options = optimoptions(@fmincon);
options.MaxFunctionEvaluations = 1e4;
disp(options)

  fmincon options:

   Options used by current Algorithm ('interior-point'):
   (Other available algorithms: 'active-set', 'sqp', 'sqp-legacy', 'trust-region-reflective')

   Set properties:
       MaxFunctionEvaluations: 10000

   Default properties:
                    Algorithm: 'interior-point'
           BarrierParamUpdate: 'monotone'
               CheckGradients: 0
          ConstraintTolerance: 1e-06
                      Display: 'final'
        EnableFeasibilityMode: 0
     FiniteDifferenceStepSize: 'sqrt(eps)'
         FiniteDifferenceType: 'forward'
         HessianApproximation: 'bfgs'
                   HessianFcn: []
           HessianMultiplyFcn: []
                  HonorBounds: 1
                MaxIterations: 1000
               ObjectiveLimit: -1e+20
          OptimalityTolerance: 1e-06
                    OutputFcn: []
                      PlotFcn: []
                 ScaleProblem: 0
    SpecifyConstraintGradient: 0
     SpecifyObjectiveGradient: 0
                StepTolerance: 1e-10
          SubproblemAlgorithm: 'factorization'
                     TypicalX: 'ones(numberOfVariables,1)'
                  UseParallel: 0

   Options not used by current Algorithm ('interior-point')
   Default properties:
    FunctionTolerance: 1e-06

[p, fval, exitflag, output] = fmincon(fnc, x0, [], [], [], [], lb, ub, @mycon, options);

Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 6.518313e-17.

Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 7.990654e-17.

Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 1.044527e-17.

Feasible point with lower objective function value found.


Local minimum possible. Constraints satisfied.

fmincon stopped because the size of the current step is less than
the value of the step size tolerance and constraints are 
satisfied to within the value of the constraint tolerance.

disp(p)

           19638.238524254
          19879.1047251019
          17226.6281214069
          6363.00448650999
           215165.60981511
          80103.5734866678
          27605.4267163278
          51439.4275828874
          20707.9005623102
         0.207884499264917
         0.180524926831855
         0.323597918952247
        0.0540865744444137
         0.233906080506567
           1156659.1631545

disp(fval)

         0.385262205496534

disp(exitflag)

     2

disp(output)

         iterations: 225
          funcCount: 3747
    constrviolation: 0
           stepsize: 1.01709150638417e-10
          algorithm: 'interior-point'
      firstorderopt: 0.0135635181978782
       cgiterations: 498
            message: '↵Local minimum possible. Constraints satisfied.↵↵fmincon stopped because the size of the current step is less than↵the value of the step size tolerance and constraints are ↵satisfied to within the value of the constraint tolerance.↵↵<stopping criteria details>↵↵Optimization stopped because the relative changes in all elements of x are↵less than options.StepTolerance = 1.000000e-10, and the relative maximum constraint↵violation, 0.000000e+00, is less than options.ConstraintTolerance = 1.000000e-06.↵↵'
       bestfeasible: [1×1 struct]

function f = Fungsi(x, t, Potcap)
   f = sum(((x(14)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)) + x(14)*(exp(-(t.*log(x(3)*x(15) + 1))/x(15)) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15)))/(x(2) - x(3)) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/((x(1) - x(3))*(x(2) - x(3)))) + x(14)*(exp(-(t.*log(x(4)*x(15) + 1))/x(15)) + (x(8)*exp(-(t.*log(x(3)*x(15) + 1))/x(15)))/(x(3) - x(4)) + (x(7)*x(8)*exp(-(t.*log(x(2)*x(15) + 1))/x(15)))/((x(2) - x(4))*(x(3) - x(4))) + (x(6)*x(7)*x(8)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/((x(1) - x(4))*(x(2) - x(4))*(x(3) - x(4)))) - x(13)*(exp(-(t.*log(x(4)*x(15) + 1))/x(15)) + (x(8)*exp(-(t.*log(x(3)*x(15) + 1))/x(15)))/(x(4) - x(5)) + (x(7)*x(8)*exp(-(t.*log(x(2)*x(15) + 1))/x(15)))/((x(3) - x(5))*(x(4) - x(5))) + (x(6)*x(7)*x(8)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5)))) - x(11)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(3))*(x(2) - x(5)))/(x(9)*(x(3) - x(4))) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(5)))/(x(9)*(x(2) - x(4))*(x(3) - x(4)))) + x(14)*(exp(-(t.*log(x(2)*x(15) + 1))/x(15)) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/(x(1) - x(2))) + x(12)*((exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(4))*(x(3) - x(5)))/(x(8)*x(9)) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(4))*(x(2) - x(5)))/(x(8)*x(9)*(x(2) - x(3))) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)*(x(1) - x(3))*(x(2) - x(3)))) - x(13)*((exp(-(t.*log(x(4)*x(15) + 1))/x(15))*(x(4) - x(5)))/x(9) + (x(8)*exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(5)))/(x(9)*(x(3) - x(4))) + (x(7)*x(8)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(5)))/(x(9)*(x(2) - x(4))*(x(3) - x(4))) + (x(6)*x(7)*x(8)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/(x(9)*(x(1) - x(4))*(x(2) - x(4))*(x(3) - x(4)))) + x(12)*((exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(4)))/(x(4) - x(5)) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(4)))/((x(3) - x(5))*(x(4) - x(5))) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5)))) - x(11)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(3))*(x(2) - x(4)))/((x(3) - x(5))*(x(4) - x(5))) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(4)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5)))) + x(14)*(exp(-(t.*log(x(5)*x(15) + 1))/x(15)) + (x(9)*exp(-(t.*log(x(4)*x(15) + 1))/x(15)))/(x(4) - x(5)) + (x(8)*x(9)*exp(-(t.*log(x(3)*x(15) + 1))/x(15)))/((x(3) - x(5))*(x(4) - x(5))) + (x(7)*x(8)*x(9)*exp(-(t.*log(x(2)*x(15) + 1))/x(15)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5))) + (x(6)*x(7)*x(8)*x(9)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/((x(1) - x(5))*(x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5)))) - x(13)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(5)))/x(9) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/(x(9)*(x(1) - x(2)))) + x(12)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(4))*(x(2) - x(5)))/(x(8)*x(9)) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)*(x(1) - x(2)))) - x(11)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(4))*(x(2) - x(5)))/(x(8)*x(9)) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)*(x(2) - x(3)))) - x(11)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(3))*(x(2) - x(4))*(x(2) - x(5)))/(x(7)*x(8)*x(9)) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(4))*(x(1) - x(5)))/(x(7)*x(8)*x(9)*(x(1) - x(2)))) - x(13)*((exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(5)))/x(9) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(5)))/(x(9)*(x(2) - x(3))) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/(x(9)*(x(1) - x(3))*(x(2) - x(3)))) + x(12)*((exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(5)))/x(9) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(5)))/(x(9)*(x(3) - x(4))) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/(x(9)*(x(2) - x(4))*(x(3) - x(4)))) - (x(13)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/x(9) + (x(12)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(2))*(x(1) - x(3))*(x(1) - x(5)))/(x(9)*(x(2) - x(4))*(x(3) - x(4))) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(2))*(x(1) - x(3))*(x(1) - x(4)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5))) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(4))*(x(1) - x(5)))/(x(7)*x(8)*x(9)) - (x(11)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(4))*(x(1) - x(5)))/(x(7)*x(8)*x(9)) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(2))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)*(x(2) - x(3))) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(2))*(x(1) - x(3))*(x(1) - x(4))*(x(1) - x(5)))/(x(6)*x(7)*x(8)*x(9)))-Potcap).^2);

end

function [c,ceq] = mycon(x)
   c = [];
   ceq = (x(10)+x(11)+x(12)+x(13)+x(14))-1;
end

[Walter Roberson]

I created a Support case about the comparatively bad results from running on MATLAB Online.

Be sure to run the above code on your own system as you might get a much better output than what is posted here.

[Rex Mantiri]

Thanks for helping me fix my code Walter!

So the only problem with my code was the constraint I guess haha. So what can I do about the inconsistent outcomes? Because the expected outcome for the parameters excluding x10-x14 (they are already constrained) are under 10. Theoretically they shouldn't have an upper bound though, that's why I put Infs in ub.

[Rex Mantiri]

I have done some reading on the warning that the code above causes and it seems that it often arises from the use of eig() so I will now post the code used to determine the expression used for the objective function to examine.

x = sym('x', [1 15], 'real')
t = sym('t', 'real')
e = [1;1;1;1;1]
A = [-x(1) x(6) 0 0 0; 0 -x(2) x(7) 0 0 ; 0 0 -x(3) x(8) 0 ; 0 0 0 -x(4) x(9) ; 0 0 0 0 -x(5)]
alpha = [x(10) x(11) x(12) x(13) x(14)]
[V, D] = eig(A);
[W, ~] = eig(A.');
lambdatopi = [log(1+x(15)*x(1))/x(15) log(1+x(15)*x(2))/x(15) log(1+x(15)*x(3))/x(15) log(1+x(15)*x(4))/x(15) log(1+x(15)*x(5))/x(15)]
Dtopi = diag(-lambdatopi)
Atopi = W*Dtopi*V
Atopit = Atopi*t
temp = [exp(Dtopi(1,1)*t) exp(Dtopi(2,2)*t) exp(Dtopi(3,3)*t) exp(Dtopi(4,4)*t) exp(Dtopi(5,5)*t)]
eDtopit = diag(temp)
R = W*eDtopit*V
Pot = alpha*R*e

where Pot is the expression in the objective function above.

The purpose of the code is to build the matrix Atopi from the left and right eigenvectors of A, and the transformed eigenvalues of A (lambdatopi). The method used for determining the left and right eigenvectors is from: https://www.mathworks.com/matlabcentral/answers/517394-get-symbolic-left-eigenvectors. Matrix Atopi is then used to make the matrix R that follows, R=exp(At). I used the method described here: https://youtu.be/l61k97RFsfs, Finally, Pot is determined by multiplying three matrices (1xn)(nxn)(nx1). Is there anything I can fix in the code above to get rid of the warning?

[Rex Mantiri]

As I was writing the comment above I saw what most likely caused the problem. It might be the inverse of matrix A used for determining the left eigenvector W. The problem is almost identical to what we see here: https://www.mathworks.com/matlabcentral/answers/1569563-why-do-i-see-a-singular-matrix-warning-here?s_tid=srchtitle. If so, is there a better way of building Atopi without inverting A?

[Walter Roberson]

x = sym('x', [1 15], 'real')

x = 

t = sym('t', 'real')

t = 

t

e = [1;1;1;1;1]

e = 5×1

1 1 1 1 1

A = [-x(1) x(6) 0 0 0; 0 -x(2) x(7) 0 0 ; 0 0 -x(3) x(8) 0 ; 0 0 0 -x(4) x(9) ; 0 0 0 0 -x(5)]

A = 

alpha = [x(10) x(11) x(12) x(13) x(14)]

alpha = 

[V, D] = eig(A);
[W, ~] = eig(A.');
lambdatopi = [log(1+x(15)*x(1))/x(15) log(1+x(15)*x(2))/x(15) log(1+x(15)*x(3))/x(15) log(1+x(15)*x(4))/x(15) log(1+x(15)*x(5))/x(15)]

lambdatopi = 

Dtopi = diag(-lambdatopi)

Dtopi = 

Atopi = W*Dtopi*V

Atopi = 

Atopit = Atopi*t

Atopit = 

temp = [exp(Dtopi(1,1)*t) exp(Dtopi(2,2)*t) exp(Dtopi(3,3)*t) exp(Dtopi(4,4)*t) exp(Dtopi(5,5)*t)]

temp = 

eDtopit = diag(temp)

eDtopit = 

R = W*eDtopit*V

R = 

Pot = alpha*R*e

Pot = 

Pots = simplify(Pot)

Pots = 

If you look at this, then you will see that you get out a definite formula, and that the formula does not itself call

SYSTEM TOO SLOW WILL TRY AGAIN LATER

[Rex Mantiri]

Oh so running one by one doesn't give the singular matrix warning huh? Does that mean the root of the problem is elsewhere?

[Rex Mantiri]

x = sym('x', [1 15], 'real')

x = 

t = sym('t', 'real')

t = 

t

A = [-x(1) x(6) 0 0 0; 0 -x(2) x(7) 0 0 ; 0 0 -x(3) x(8) 0 ; 0 0 0 -x(4) x(9) ; 0 0 0 0 -x(5)]

A = 

B = A.'

B = 

It is in fact invertible. I am stumped again hahaha.

[Walter Roberson]

Sorry, system was way too slow to use earlier.

If you look at the Pot and Pots formulas, you will see that they do not use eig() or \ or / itself. The RCOND message you are seeing is from the gradient estimation or the Hessian estimation, not from your function itself. Using a different Algorithm might help, if any of the other ones are suitable.

However, look again at the Pots formula, and notice that it involves divisions by

x6, x7, x8, x9, individually, and by every combination of x1, x2, x3, x4, x5 minus a different member of x1, x2, x3, x4, x5 . This means that you need to provide positive lower bounds for x6, x7, x8, x9, and that you need to ensure that x1, x2, x3, x4, x5 cannot equal each other.

Saying that two variables cannot equal each other is a bit tricky. Algebraically you could say that A<B | -A<-B -- but you cannot "or" constraints, and you also cannot express a pure < constraint. A-B<0 | B-A<0 is the same, and is just a rewriting of the above.

When two variables cannot be equal, it is often easiest to configure that one must be less than the other... where A<B ends up having to be expressed as A-B<=-eps(realmin). And in this case, you need to figure out which of the variables needs to be less than the other. Although the above LaTex only shows lower numbered variable minus higher numbered variable, you would have to look closely at the signs of the terms because MATLAB converts (x3-x2) into -(x2-x3) in some cases... and the subtractions in the numerator matter too as the signs can cancel out between numerator and denominator...

Sometimes the easiest way is just try all of the different orders and see which one gives the best result... Unless, that is, you have external knowledge of the situation that allows you to impose a full or partial sort.

[Rex Mantiri]

Wow that sounds like a really hard and time consuming solution. But you are correct. Theoretically x1-x5 have to be distinct. I also cannot provide positive lower bounds for x6-x9 because they are values in the interval [0,Inf). Sorting x1-x5 using external knowledge is also impossible as the only knowledge I have of these parameters are that they are distinct. Considering all of the above what do you suggest I do to try running this?

Also, what do you mean by "you also cannot express a pure < constraint. A-B<0 | B-A<0 is the same, and is just a rewriting of the above."?

[Walter Roberson]

A.' is not the inverse of A.

If you take inv(A) and examine the terms it has division by 0 if any of x1 through x5 are 0. You must impose positive boundaries for the general calculation to be valid.

[Rex Mantiri]

Oh right. So how would I impose such boundaries?

[Walter Roberson]

Use a positive value in the lb vector.

In this case I would suggest no smaller than eps(realmin)^(1/5) to avoid underflow when multiplying values together.

[Rex Mantiri]

Oh that's a good idea! I'm still a beginner, so may I ask how I could implement that into lb specifically? Because if I really have to put a positive value as the lower bound I would like to have the lowest possible value so I don't betray the theory too much.

Also, this kind of fix still doesn't address the distinct x1-x5 problem right? Is it necessary to also find a solution for that or not?

[Walter Roberson]

We know from my Answer above that we can do even better than the below; this shows what happens if you make x1 < x2 < x3 < x4 < x5

format long g
Potcap = [0.986702168; 0.97272091; 0.957930961; 0.942424001; 0.926404439; 0.909375829; 0.891635315; 0.873329497; 0.854253377; 0.834442537; 0.813592045; 0.791234153; 0.768357994; 0.744306568; 0.719094568; 0.692488019; 0.66411648; 0.634292184; 0.602498593; 0.569711546; 0.534931653];
t = [1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20;21];
x0 = [0.2;0.21;0.22;0.23;0.24;0.31;0.32;0.33;0.34;0.1;0.1;0.1;0.1;0.1;0.3];
N = length(x0);

A = zeros(4,N);
A(1,1) = 1; A(2,2) = 1; A(3,3) = 1; A(4,4) = 1;
A(1,2) = -1; A(2,3) = -1; A(3,4) = -1; A(4,5) = -1;
b(1:4,1) = -eps(realmin);
A, b

A = 4×15

1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0

b = 4×1

1.0e+00 * -4.94065645841247e-324 -4.94065645841247e-324 -4.94065645841247e-324 -4.94065645841247e-324

lb = zeros(15,1); lb(1:9) = eps(realmin)^(1/5);
ub = [Inf Inf Inf Inf Inf Inf Inf Inf Inf 1 1 1 1 1 Inf];
fnc = @(x) Fungsi(x,t,Potcap);

options = optimoptions(@fmincon);
options.MaxFunctionEvaluations = 1e4;
disp(options)

  fmincon options:

   Options used by current Algorithm ('interior-point'):
   (Other available algorithms: 'active-set', 'sqp', 'sqp-legacy', 'trust-region-reflective')

   Set properties:
       MaxFunctionEvaluations: 10000

   Default properties:
                    Algorithm: 'interior-point'
           BarrierParamUpdate: 'monotone'
               CheckGradients: 0
          ConstraintTolerance: 1e-06
                      Display: 'final'
        EnableFeasibilityMode: 0
     FiniteDifferenceStepSize: 'sqrt(eps)'
         FiniteDifferenceType: 'forward'
         HessianApproximation: 'bfgs'
                   HessianFcn: []
           HessianMultiplyFcn: []
                  HonorBounds: 1
                MaxIterations: 1000
               ObjectiveLimit: -1e+20
          OptimalityTolerance: 1e-06
                    OutputFcn: []
                      PlotFcn: []
                 ScaleProblem: 0
    SpecifyConstraintGradient: 0
     SpecifyObjectiveGradient: 0
                StepTolerance: 1e-10
          SubproblemAlgorithm: 'factorization'
                     TypicalX: 'ones(numberOfVariables,1)'
                  UseParallel: 0

   Options not used by current Algorithm ('interior-point')
   Default properties:
    FunctionTolerance: 1e-06

[p, fval, exitflag, output] = fmincon(fnc, x0, A, b, [], [], lb, ub, @mycon, options);

Feasible point with lower objective function value found.


Local minimum possible. Constraints satisfied.

fmincon stopped because the size of the current step is less than
the value of the step size tolerance and constraints are 
satisfied to within the value of the constraint tolerance.

disp(p)

          1.43488281245735
          1.52016412760507
          2.62390116472478
          2.90213914906372
          3.13878858211083
          3.98446630617199
            7.249951957201
         0.752617484931841
          1.38431609480644
         0.207530286887786
         0.197770267936923
         0.171378604985807
         0.198755084294404
          0.22456575589508
          236.762038172939

disp(fval)

        0.0348765044445815

disp(exitflag)

     2

disp(output)

         iterations: 184
          funcCount: 3281
    constrviolation: 2.22044604925031e-16
           stepsize: 1.36626434969871e-09
          algorithm: 'interior-point'
      firstorderopt: 0.0659210247902407
       cgiterations: 803
            message: '↵Local minimum possible. Constraints satisfied.↵↵fmincon stopped because the size of the current step is less than↵the value of the step size tolerance and constraints are ↵satisfied to within the value of the constraint tolerance.↵↵<stopping criteria details>↵↵Optimization stopped because the relative changes in all elements of x are↵less than options.StepTolerance = 1.000000e-10, and the relative maximum constraint↵violation, 2.220446e-16, is less than options.ConstraintTolerance = 1.000000e-06.↵↵'
       bestfeasible: [1×1 struct]

function f = Fungsi(x, t, Potcap)
   f = sum(((x(14)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)) + x(14)*(exp(-(t.*log(x(3)*x(15) + 1))/x(15)) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15)))/(x(2) - x(3)) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/((x(1) - x(3))*(x(2) - x(3)))) + x(14)*(exp(-(t.*log(x(4)*x(15) + 1))/x(15)) + (x(8)*exp(-(t.*log(x(3)*x(15) + 1))/x(15)))/(x(3) - x(4)) + (x(7)*x(8)*exp(-(t.*log(x(2)*x(15) + 1))/x(15)))/((x(2) - x(4))*(x(3) - x(4))) + (x(6)*x(7)*x(8)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/((x(1) - x(4))*(x(2) - x(4))*(x(3) - x(4)))) - x(13)*(exp(-(t.*log(x(4)*x(15) + 1))/x(15)) + (x(8)*exp(-(t.*log(x(3)*x(15) + 1))/x(15)))/(x(4) - x(5)) + (x(7)*x(8)*exp(-(t.*log(x(2)*x(15) + 1))/x(15)))/((x(3) - x(5))*(x(4) - x(5))) + (x(6)*x(7)*x(8)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5)))) - x(11)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(3))*(x(2) - x(5)))/(x(9)*(x(3) - x(4))) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(5)))/(x(9)*(x(2) - x(4))*(x(3) - x(4)))) + x(14)*(exp(-(t.*log(x(2)*x(15) + 1))/x(15)) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/(x(1) - x(2))) + x(12)*((exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(4))*(x(3) - x(5)))/(x(8)*x(9)) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(4))*(x(2) - x(5)))/(x(8)*x(9)*(x(2) - x(3))) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)*(x(1) - x(3))*(x(2) - x(3)))) - x(13)*((exp(-(t.*log(x(4)*x(15) + 1))/x(15))*(x(4) - x(5)))/x(9) + (x(8)*exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(5)))/(x(9)*(x(3) - x(4))) + (x(7)*x(8)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(5)))/(x(9)*(x(2) - x(4))*(x(3) - x(4))) + (x(6)*x(7)*x(8)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/(x(9)*(x(1) - x(4))*(x(2) - x(4))*(x(3) - x(4)))) + x(12)*((exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(4)))/(x(4) - x(5)) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(4)))/((x(3) - x(5))*(x(4) - x(5))) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5)))) - x(11)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(3))*(x(2) - x(4)))/((x(3) - x(5))*(x(4) - x(5))) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(4)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5)))) + x(14)*(exp(-(t.*log(x(5)*x(15) + 1))/x(15)) + (x(9)*exp(-(t.*log(x(4)*x(15) + 1))/x(15)))/(x(4) - x(5)) + (x(8)*x(9)*exp(-(t.*log(x(3)*x(15) + 1))/x(15)))/((x(3) - x(5))*(x(4) - x(5))) + (x(7)*x(8)*x(9)*exp(-(t.*log(x(2)*x(15) + 1))/x(15)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5))) + (x(6)*x(7)*x(8)*x(9)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/((x(1) - x(5))*(x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5)))) - x(13)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(5)))/x(9) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/(x(9)*(x(1) - x(2)))) + x(12)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(4))*(x(2) - x(5)))/(x(8)*x(9)) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)*(x(1) - x(2)))) - x(11)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(4))*(x(2) - x(5)))/(x(8)*x(9)) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)*(x(2) - x(3)))) - x(11)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(3))*(x(2) - x(4))*(x(2) - x(5)))/(x(7)*x(8)*x(9)) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(4))*(x(1) - x(5)))/(x(7)*x(8)*x(9)*(x(1) - x(2)))) - x(13)*((exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(5)))/x(9) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(5)))/(x(9)*(x(2) - x(3))) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/(x(9)*(x(1) - x(3))*(x(2) - x(3)))) + x(12)*((exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(5)))/x(9) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(5)))/(x(9)*(x(3) - x(4))) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/(x(9)*(x(2) - x(4))*(x(3) - x(4)))) - (x(13)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/x(9) + (x(12)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(2))*(x(1) - x(3))*(x(1) - x(5)))/(x(9)*(x(2) - x(4))*(x(3) - x(4))) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(2))*(x(1) - x(3))*(x(1) - x(4)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5))) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(4))*(x(1) - x(5)))/(x(7)*x(8)*x(9)) - (x(11)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(4))*(x(1) - x(5)))/(x(7)*x(8)*x(9)) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(2))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)*(x(2) - x(3))) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(2))*(x(1) - x(3))*(x(1) - x(4))*(x(1) - x(5)))/(x(6)*x(7)*x(8)*x(9)))-Potcap).^2);

end

function [c,ceq] = mycon(x)
   c = [];
   ceq = (x(10)+x(11)+x(12)+x(13)+x(14))-1;
end

[Rex Mantiri]

Hmm... Okay I think I understand the code you have given. So you are saying that I should try with other combinations of sorting x1-x5 until I find the best outcome right? The question is how would I know which outcome is the best fit for the data if the only prior knowledge I have for those parameters is what I have given above? Is there any objective way of ranking each solution by their fit?

Also does the command assume(x1~=x2) not work for the problem of distinct parameters?

[Rex Mantiri]

format long g
x = sym('x', [1 15], 'real')

x = 

assume(x(1)~=x(2))
assume(x(1)~=x(3))
assume(x(1)~=x(4))
assume(x(1)~=x(5))
assume(x(2)~=x(3))
assume(x(2)~=x(4))
assume(x(2)~=x(5))
assume(x(3)~=x(4))
assume(x(3)~=x(5))
assume(x(4)~=x(5))
Potcap = [0.986702168; 0.97272091; 0.957930961; 0.942424001; 0.926404439; 0.909375829; 0.891635315; 0.873329497; 0.854253377; 0.834442537; 0.813592045; 0.791234153; 0.768357994; 0.744306568; 0.719094568; 0.692488019; 0.66411648; 0.634292184; 0.602498593; 0.569711546; 0.534931653];
t = [1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20;21];
x0 = [0.2;0.21;0.22;0.23;0.24;0.31;0.32;0.33;0.34;0.1;0.1;0.1;0.1;0.1;0.3];
lb = zeros(15,1); lb(1:9) = eps(realmin)^(1/5);
ub = [Inf Inf Inf Inf Inf Inf Inf Inf Inf 1 1 1 1 1 Inf];
fnc = @(x) Fungsi(x,t,Potcap);
options = optimoptions(@fmincon);
options.MaxFunctionEvaluations = 1e4;
disp(options)

  fmincon options:

   Options used by current Algorithm ('interior-point'):
   (Other available algorithms: 'active-set', 'sqp', 'sqp-legacy', 'trust-region-reflective')

   Set properties:
       MaxFunctionEvaluations: 10000

   Default properties:
                    Algorithm: 'interior-point'
           BarrierParamUpdate: 'monotone'
               CheckGradients: 0
          ConstraintTolerance: 1e-06
                      Display: 'final'
        EnableFeasibilityMode: 0
     FiniteDifferenceStepSize: 'sqrt(eps)'
         FiniteDifferenceType: 'forward'
         HessianApproximation: 'bfgs'
                   HessianFcn: []
           HessianMultiplyFcn: []
                  HonorBounds: 1
                MaxIterations: 1000
               ObjectiveLimit: -1e+20
          OptimalityTolerance: 1e-06
                    OutputFcn: []
                      PlotFcn: []
                 ScaleProblem: 0
    SpecifyConstraintGradient: 0
     SpecifyObjectiveGradient: 0
                StepTolerance: 1e-10
          SubproblemAlgorithm: 'factorization'
                     TypicalX: 'ones(numberOfVariables,1)'
                  UseParallel: 0

   Options not used by current Algorithm ('interior-point')
   Default properties:
    FunctionTolerance: 1e-06

[p, fval, exitflag, output] = fmincon(fnc, x0, [], [], [], [], lb, ub, @mycon, options)

Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 6.518313e-17.

Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 7.990654e-17.

Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 1.044527e-17.

Feasible point with lower objective function value found.


Local minimum possible. Constraints satisfied.

fmincon stopped because the size of the current step is less than
the value of the step size tolerance and constraints are 
satisfied to within the value of the constraint tolerance.

p = 15×1

1.0e+00 * 19638.238524254 19879.1047251019 17226.6281214069 6363.00448650999 215165.60981511 80103.5734866678 27605.4267163278 51439.4275828874 20707.9005623102 0.207884499264917

fval = 
         0.385262205496534

exitflag = 
     2

output = struct with fields:
         iterations: 225
          funcCount: 3747
    constrviolation: 0
           stepsize: 1.01709150638417e-10
          algorithm: 'interior-point'
      firstorderopt: 0.0135635181978782
       cgiterations: 498
            message: '↵Local minimum possible. Constraints satisfied.↵↵fmincon stopped because the size of the current step is less than↵the value of the step size tolerance and constraints are ↵satisfied to within the value of the constraint tolerance.↵↵<stopping criteria details>↵↵Optimization stopped because the relative changes in all elements of x are↵less than options.StepTolerance = 1.000000e-10, and the relative maximum constraint↵violation, 0.000000e+00, is less than options.ConstraintTolerance = 1.000000e-06.↵↵'
       bestfeasible: [1×1 struct]

function f = Fungsi(x, t, Potcap)
   f = sum(((x(14)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)) + x(14)*(exp(-(t.*log(x(3)*x(15) + 1))/x(15)) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15)))/(x(2) - x(3)) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/((x(1) - x(3))*(x(2) - x(3)))) + x(14)*(exp(-(t.*log(x(4)*x(15) + 1))/x(15)) + (x(8)*exp(-(t.*log(x(3)*x(15) + 1))/x(15)))/(x(3) - x(4)) + (x(7)*x(8)*exp(-(t.*log(x(2)*x(15) + 1))/x(15)))/((x(2) - x(4))*(x(3) - x(4))) + (x(6)*x(7)*x(8)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/((x(1) - x(4))*(x(2) - x(4))*(x(3) - x(4)))) - x(13)*(exp(-(t.*log(x(4)*x(15) + 1))/x(15)) + (x(8)*exp(-(t.*log(x(3)*x(15) + 1))/x(15)))/(x(4) - x(5)) + (x(7)*x(8)*exp(-(t.*log(x(2)*x(15) + 1))/x(15)))/((x(3) - x(5))*(x(4) - x(5))) + (x(6)*x(7)*x(8)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5)))) - x(11)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(3))*(x(2) - x(5)))/(x(9)*(x(3) - x(4))) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(5)))/(x(9)*(x(2) - x(4))*(x(3) - x(4)))) + x(14)*(exp(-(t.*log(x(2)*x(15) + 1))/x(15)) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/(x(1) - x(2))) + x(12)*((exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(4))*(x(3) - x(5)))/(x(8)*x(9)) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(4))*(x(2) - x(5)))/(x(8)*x(9)*(x(2) - x(3))) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)*(x(1) - x(3))*(x(2) - x(3)))) - x(13)*((exp(-(t.*log(x(4)*x(15) + 1))/x(15))*(x(4) - x(5)))/x(9) + (x(8)*exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(5)))/(x(9)*(x(3) - x(4))) + (x(7)*x(8)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(5)))/(x(9)*(x(2) - x(4))*(x(3) - x(4))) + (x(6)*x(7)*x(8)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/(x(9)*(x(1) - x(4))*(x(2) - x(4))*(x(3) - x(4)))) + x(12)*((exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(4)))/(x(4) - x(5)) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(4)))/((x(3) - x(5))*(x(4) - x(5))) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5)))) - x(11)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(3))*(x(2) - x(4)))/((x(3) - x(5))*(x(4) - x(5))) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(4)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5)))) + x(14)*(exp(-(t.*log(x(5)*x(15) + 1))/x(15)) + (x(9)*exp(-(t.*log(x(4)*x(15) + 1))/x(15)))/(x(4) - x(5)) + (x(8)*x(9)*exp(-(t.*log(x(3)*x(15) + 1))/x(15)))/((x(3) - x(5))*(x(4) - x(5))) + (x(7)*x(8)*x(9)*exp(-(t.*log(x(2)*x(15) + 1))/x(15)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5))) + (x(6)*x(7)*x(8)*x(9)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/((x(1) - x(5))*(x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5)))) - x(13)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(5)))/x(9) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/(x(9)*(x(1) - x(2)))) + x(12)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(4))*(x(2) - x(5)))/(x(8)*x(9)) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)*(x(1) - x(2)))) - x(11)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(4))*(x(2) - x(5)))/(x(8)*x(9)) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)*(x(2) - x(3)))) - x(11)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(3))*(x(2) - x(4))*(x(2) - x(5)))/(x(7)*x(8)*x(9)) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(4))*(x(1) - x(5)))/(x(7)*x(8)*x(9)*(x(1) - x(2)))) - x(13)*((exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(5)))/x(9) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(5)))/(x(9)*(x(2) - x(3))) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/(x(9)*(x(1) - x(3))*(x(2) - x(3)))) + x(12)*((exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(5)))/x(9) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(5)))/(x(9)*(x(3) - x(4))) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/(x(9)*(x(2) - x(4))*(x(3) - x(4)))) - (x(13)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/x(9) + (x(12)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(2))*(x(1) - x(3))*(x(1) - x(5)))/(x(9)*(x(2) - x(4))*(x(3) - x(4))) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(2))*(x(1) - x(3))*(x(1) - x(4)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5))) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(4))*(x(1) - x(5)))/(x(7)*x(8)*x(9)) - (x(11)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(4))*(x(1) - x(5)))/(x(7)*x(8)*x(9)) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(2))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)*(x(2) - x(3))) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(2))*(x(1) - x(3))*(x(1) - x(4))*(x(1) - x(5)))/(x(6)*x(7)*x(8)*x(9)))-Potcap).^2);
end
function [c,ceq] = mycon(x)
   c = [];
   ceq = (x(10)+x(11)+x(12)+x(13)+x(14))-1;
end

Oh it doesn't seem to solve the problem at all.

[Walter Roberson]

x = sym('x', [1 15], 'real')
assume(x(1)~=x(2))
assume(x(1)~=x(3))
assume(x(1)~=x(4))
assume(x(1)~=x(5))
assume(x(2)~=x(3))
assume(x(2)~=x(4))
assume(x(2)~=x(5))
assume(x(3)~=x(4))
assume(x(3)~=x(5))
assume(x(4)~=x(5))

Okay, you created a bunch of symbolic variables and gave some assumptions to them.

Potcap = [0.986702168; 0.97272091; 0.957930961; 0.942424001; 0.926404439; 0.909375829; 0.891635315; 0.873329497; 0.854253377; 0.834442537; 0.813592045; 0.791234153; 0.768357994; 0.744306568; 0.719094568; 0.692488019; 0.66411648; 0.634292184; 0.602498593; 0.569711546; 0.534931653];
t = [1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20;21];
x0 = [0.2;0.21;0.22;0.23;0.24;0.31;0.32;0.33;0.34;0.1;0.1;0.1;0.1;0.1;0.3];
lb = zeros(15,1); lb(1:9) = eps(realmin)^(1/5);
ub = [Inf Inf Inf Inf Inf Inf Inf Inf Inf 1 1 1 1 1 Inf];

None of those lines use the symbolic variables.

fnc = @(x) Fungsi(x,t,Potcap);

That creates an anonymous function. There is no connection between the symbolic x and the x that appears in fnc. The fnc you created is almost the same as

fnc = @(varargin) Fungsi(varargin{1}, t, Potcap)

in that it takes whatever is passed in as the first parameter to the anonymous function, and calls Fungsi with that parameter and two other parameters. (The version with @(x) will complain if you pass more than one parameter in the call to fnc where the varargin will not complain... and some differences in what argname() returns.) All variables inside @() construct for anonymous functions are "dummy parameter names", used only to identify which input parameters get passed to where in the expressions; the names inside @() "shadow" any meaning that the same name might have outside. As far as MATLAB is concerned, you might as well have defined

fnc = @(GodzillaVsMothra) Fungsi(GodzillaVsMothra, t, Potcap)

and the existing symbolic x would have the same effect on the function call -- which is to say no effect. The symbolic x has no connection to the processing of the fnc that you defined.

options = optimoptions(@fmincon);
options.MaxFunctionEvaluations = 1e4;
disp(options)

Those do not use the symbolic x either.

[p, fval, exitflag, output] = fmincon(fnc, x0, [], [], [], [], lb, ub, @mycon, options)

No symbolic x used there.

function f = Fungsi(x, t, Potcap)
   f = sum(((x(14)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)) + x(14)*(exp(-(t.*log(x(3)*x(15) + 1))/x(15)) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15)))/(x(2) - x(3)) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/((x(1) - x(3))*(x(2) - x(3)))) + x(14)*(exp(-(t.*log(x(4)*x(15) + 1))/x(15)) + (x(8)*exp(-(t.*log(x(3)*x(15) + 1))/x(15)))/(x(3) - x(4)) + (x(7)*x(8)*exp(-(t.*log(x(2)*x(15) + 1))/x(15)))/((x(2) - x(4))*(x(3) - x(4))) + (x(6)*x(7)*x(8)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/((x(1) - x(4))*(x(2) - x(4))*(x(3) - x(4)))) - x(13)*(exp(-(t.*log(x(4)*x(15) + 1))/x(15)) + (x(8)*exp(-(t.*log(x(3)*x(15) + 1))/x(15)))/(x(4) - x(5)) + (x(7)*x(8)*exp(-(t.*log(x(2)*x(15) + 1))/x(15)))/((x(3) - x(5))*(x(4) - x(5))) + (x(6)*x(7)*x(8)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5)))) - x(11)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(3))*(x(2) - x(5)))/(x(9)*(x(3) - x(4))) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(5)))/(x(9)*(x(2) - x(4))*(x(3) - x(4)))) + x(14)*(exp(-(t.*log(x(2)*x(15) + 1))/x(15)) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/(x(1) - x(2))) + x(12)*((exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(4))*(x(3) - x(5)))/(x(8)*x(9)) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(4))*(x(2) - x(5)))/(x(8)*x(9)*(x(2) - x(3))) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)*(x(1) - x(3))*(x(2) - x(3)))) - x(13)*((exp(-(t.*log(x(4)*x(15) + 1))/x(15))*(x(4) - x(5)))/x(9) + (x(8)*exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(5)))/(x(9)*(x(3) - x(4))) + (x(7)*x(8)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(5)))/(x(9)*(x(2) - x(4))*(x(3) - x(4))) + (x(6)*x(7)*x(8)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/(x(9)*(x(1) - x(4))*(x(2) - x(4))*(x(3) - x(4)))) + x(12)*((exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(4)))/(x(4) - x(5)) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(4)))/((x(3) - x(5))*(x(4) - x(5))) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5)))) - x(11)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(3))*(x(2) - x(4)))/((x(3) - x(5))*(x(4) - x(5))) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(4)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5)))) + x(14)*(exp(-(t.*log(x(5)*x(15) + 1))/x(15)) + (x(9)*exp(-(t.*log(x(4)*x(15) + 1))/x(15)))/(x(4) - x(5)) + (x(8)*x(9)*exp(-(t.*log(x(3)*x(15) + 1))/x(15)))/((x(3) - x(5))*(x(4) - x(5))) + (x(7)*x(8)*x(9)*exp(-(t.*log(x(2)*x(15) + 1))/x(15)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5))) + (x(6)*x(7)*x(8)*x(9)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)))/((x(1) - x(5))*(x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5)))) - x(13)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(5)))/x(9) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/(x(9)*(x(1) - x(2)))) + x(12)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(4))*(x(2) - x(5)))/(x(8)*x(9)) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)*(x(1) - x(2)))) - x(11)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(4))*(x(2) - x(5)))/(x(8)*x(9)) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)*(x(2) - x(3)))) - x(11)*((exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(3))*(x(2) - x(4))*(x(2) - x(5)))/(x(7)*x(8)*x(9)) + (x(6)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(4))*(x(1) - x(5)))/(x(7)*x(8)*x(9)*(x(1) - x(2)))) - x(13)*((exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(5)))/x(9) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(5)))/(x(9)*(x(2) - x(3))) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/(x(9)*(x(1) - x(3))*(x(2) - x(3)))) + x(12)*((exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(3) - x(5)))/x(9) + (x(7)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(x(2) - x(5)))/(x(9)*(x(3) - x(4))) + (x(6)*x(7)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/(x(9)*(x(2) - x(4))*(x(3) - x(4)))) - (x(13)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(5)))/x(9) + (x(12)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(2))*(x(1) - x(3))*(x(1) - x(5)))/(x(9)*(x(2) - x(4))*(x(3) - x(4))) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(2))*(x(1) - x(3))*(x(1) - x(4)))/((x(2) - x(5))*(x(3) - x(5))*(x(4) - x(5))) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(4))*(x(1) - x(5)))/(x(7)*x(8)*x(9)) - (x(11)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(3))*(x(1) - x(4))*(x(1) - x(5)))/(x(7)*x(8)*x(9)) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(2))*(x(1) - x(4))*(x(1) - x(5)))/(x(8)*x(9)*(x(2) - x(3))) + (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*(x(1) - x(2))*(x(1) - x(3))*(x(1) - x(4))*(x(1) - x(5)))/(x(6)*x(7)*x(8)*x(9)))-Potcap).^2);
end
function [c,ceq] = mycon(x)
   c = [];
   ceq = (x(10)+x(11)+x(12)+x(13)+x(14))-1;
end

For those two functions, x is the local name for whatever was passed in as the first parameter to the function. Which, as explained earlier, has nothing to do with the symbolic x.

We have now reached the end of the code, and the symbolic x with its assumptions have no effect on the calculations.

Perhaps you would be more comfortable using the Problem Based Optimization workflow, https://www.mathworks.com/help/optim/ug/problem-based-workflow.html

However, that workflow does not support ~= and while it supports == and <= and >= it does not support < or > by themselves. Sometimes you can force constructs to do unusual things by using additional "indicator" variables .

[Rex Mantiri]

I had a feeling that was the case. So for my particular case would you recommend sticking to fmincon or switching to problem based optimization for the estimation? And if you recommend fmincon what method of ranking solutions should I use?

[Walter Roberson]

It would be a lot faster to do all of the calculations than to worry about how to do it some super-great way.

N = length(x0);

sets = perms(1:5);
Nsets = size(sets,1);
sets(1:5,:)

ans = 5×5

5 4 3 2 1 5 4 3 1 2 5 4 2 3 1 5 4 2 1 3 5 4 1 3 2

bestx = nan(1,N);
bestfval = inf;
bestperm = nan(1,5);
for K = 1 : Nsets
   ts = sets(K,:);
   A = zeros(4,N);
   A(sub2ind(size(A), 1:4, ts(1:4))) = 1;
   A(sub2ind(size(A), 1:4, ts(2:5))) = -1;
   b(1:4,1) = -eps(realmin);
   [p, fval, exitflag, output] = fmincon(fnc, x0, A, b, [], [], lb, ub, @mycon, options);
   if exitflag < 0; continue; end   %do not record if there was a failure
   if fval == bestfval
      bestx = [bestx; p(:).'];
      bestperm = [bestperm; ts];
      fprintf('permutation [%d,%d,%d,%d,%d] equaled fval %g\n', ts, fval);
   elseif fval < bestfval
       bestx = p(:).';
       bestperm = ts;
       bestfval = fval;
       fprintf('permutation [%d,%d,%d,%d,%d] improved fval to %g\n', ts, fval);
   end
end

At the end of this, bestfval will be a scalar -- inf if no successes, and otherwise the minimum found. bestx will have one row of x values for each permutation that resulted in the (exact) same optimal fval. bestperm will have one row of constraint orders for each permutation that resulted in the (exact) same optimal fval.

A permutation such as 5 4 1 3 2 means x5 < x4 < x1 < x3 < x2 as a constraint.

It doesn't matter if it takes half an hour to execute: the task will still be done a lot faster than us going back and forth trying to come up with smart ways to do better. Especially as it is 3:30AM where I am...

[Rex Mantiri]

Wow that looks like an amazing piece of code and I need a minute to try to understand it. I'm sorry for taking up so much of your time. Thank you very much for all the help today Walter!

[Rex Mantiri]

@Walter Roberson I made a mistake in forming the objective function. In my code above, W*Dtopi*V is the wrong way to construct the matrix Atopi. I have found that the correct way to build a matrix from eigenvectors and eigenvalues is V*Dtopi/V

test = [0 5; -1 6]

test = 2×2

0 5 -1 6

[testV, testD] = eig(test)

testV = 2×2

-0.9806 -0.7071 -0.1961 -0.7071

testD = 2×2

1 0 0 5

reconstest = testV*testD/testV

reconstest = 2×2

-0.0000 5.0000 -1.0000 6.0000

The problem is, after I have determined the correct form of the objective function, evaluating it meets an error with '.*'. The fixed version of Pot is:

newPot = x10*exp(-(t*log(x1*x15 + 1))/x15) + x11*exp(-(t*log(x2*x15 + 1))/x15) + x12*exp(-(t*log(x3*x15 + 1))/x15) + x13*exp(-(t*log(x4*x15 + 1))/x15) + x14*exp(-(t*log(x5*x15 + 1))/x15) + (x13*exp(-(t*log(x4*x15 + 1))/x15)*exp(-(t*log(x5*x15 + 1))/x15)*(x9*exp((t*log(x4*x15 + 1))/x15) - x9*exp((t*log(x5*x15 + 1))/x15)))/(x4 - x5) + (x6*x10*exp(-(t*log(x1*x15 + 1))/x15)*exp(-(t*log(x2*x15 + 1))/x15)*(exp((t*log(x1*x15 + 1))/x15) - exp((t*log(x2*x15 + 1))/x15)))/(x1 - x2) + (x7*x11*exp(-(t*log(x2*x15 + 1))/x15)*exp(-(t*log(x3*x15 + 1))/x15)*(exp((t*log(x2*x15 + 1))/x15) - exp((t*log(x3*x15 + 1))/x15)))/(x2 - x3) + (x8*x12*exp(-(t*log(x3*x15 + 1))/x15)*exp(-(t*log(x4*x15 + 1))/x15)*(exp((t*log(x3*x15 + 1))/x15) - exp((t*log(x4*x15 + 1))/x15)))/(x3 - x4) + (x12*exp(-(t*log(x3*x15 + 1))/x15)*exp(-(t*log(x4*x15 + 1))/x15)*exp(-(t*log(x5*x15 + 1))/x15)*(x3*x8*x9*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x3*x8*x9*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x4*x8*x9*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x4*x8*x9*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x5*x8*x9*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x5*x8*x9*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15)))/((x3 - x4)*(x3 - x5)*(x4 - x5)) + (x6*x7*x10*exp(-(t*log(x1*x15 + 1))/x15)*exp(-(t*log(x2*x15 + 1))/x15)*exp(-(t*log(x3*x15 + 1))/x15)*(x1*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15) - x1*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15) - x2*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15) + x2*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15) + x3*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15) - x3*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)))/((x1 - x2)*(x1 - x3)*(x2 - x3)) + (x7*x8*x11*exp(-(t*log(x2*x15 + 1))/x15)*exp(-(t*log(x3*x15 + 1))/x15)*exp(-(t*log(x4*x15 + 1))/x15)*(x2*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15) - x2*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x3*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15) + x3*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x4*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x4*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)))/((x2 - x3)*(x2 - x4)*(x3 - x4)) - (x11*exp(-(t*log(x2*x15 + 1))/x15)*exp(-(t*log(x3*x15 + 1))/x15)*exp(-(t*log(x4*x15 + 1))/x15)*exp(-(t*log(x5*x15 + 1))/x15)*(x2*x3^2*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x2^2*x3*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x2*x3^2*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2*x4^2*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x2^2*x3*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^2*x4*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x3*x4^2*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x3^2*x4*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x2*x4^2*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2*x5^2*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2^2*x4*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2^2*x5*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2*x5^2*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x3*x5^2*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^2*x5*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x3^2*x5*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x3*x4^2*x7*x8*x9*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x3^2*x4*x7*x8*x9*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x3*x5^2*x7*x8*x9*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x4*x5^2*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x3^2*x5*x7*x8*x9*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x4^2*x5*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x4*x5^2*x7*x8*x9*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x4^2*x5*x7*x8*x9*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15)))/((x2 - x3)*(x2 - x4)*(x2 - x5)*(x3 - x4)*(x3 - x5)*(x4 - x5)) - (x6*x7*x8*x10*exp(-(t*log(x1*x15 + 1))/x15)*exp(-(t*log(x2*x15 + 1))/x15)*exp(-(t*log(x3*x15 + 1))/x15)*exp(-(t*log(x4*x15 + 1))/x15)*(x1*x2^2*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15) - x1^2*x2*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15) - x1*x2^2*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1*x3^2*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15) + x1^2*x2*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x1^2*x3*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15) + x2*x3^2*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15) - x2^2*x3*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15) + x1*x3^2*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x1*x4^2*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1^2*x3*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1^2*x4*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1*x4^2*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x2*x4^2*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x1^2*x4*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x2^2*x4*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x2*x3^2*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x2^2*x3*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x2*x4^2*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x3*x4^2*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x2^2*x4*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x3^2*x4*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x3*x4^2*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x3^2*x4*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)))/((x1 - x2)*(x1 - x3)*(x1 - x4)*(x2 - x3)*(x2 - x4)*(x3 - x4)) - (x10*exp(-(t*log(x1*x15 + 1))/x15)*exp(-(t*log(x2*x15 + 1))/x15)*exp(-(t*log(x3*x15 + 1))/x15)*exp(-(t*log(x4*x15 + 1))/x15)*exp(-(t*log(x5*x15 + 1))/x15)*(x1*x2^2*x3^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1*x2^3*x3^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1^2*x2*x3^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x1^2*x2^3*x3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x1^3*x2*x3^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1^3*x2^2*x3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1*x2^2*x3^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1*x2^2*x4^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x1*x2^3*x3^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1*x2^3*x4^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x1^2*x2*x3^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^2*x2*x4^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1^2*x2^3*x3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^2*x2^3*x4*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1^3*x2*x3^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^3*x2*x4^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x1^3*x2^2*x3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^3*x2^2*x4*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x1*x3^2*x4^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1*x3^3*x4^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1^2*x3*x4^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x1^2*x3^3*x4*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x1^3*x3*x4^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1^3*x3^2*x4*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x1*x2^2*x4^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1*x2^2*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1*x2^3*x4^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1*x2^3*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2*x3^2*x4^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x2*x3^3*x4^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1^2*x2*x4^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^2*x2*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^2*x2^3*x4*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^2*x2^3*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^3*x2*x4^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^3*x2*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^3*x2^2*x4*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^3*x2^2*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^2*x3*x4^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x2^2*x3^3*x4*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x2^3*x3*x4^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x2^3*x3^2*x4*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1*x2^2*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1*x2^3*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1*x3^2*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1*x3^3*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^2*x2*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^2*x3*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^2*x2^3*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^2*x3^3*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^3*x2*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^3*x3*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^3*x2^2*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^3*x3^2*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1*x3^2*x4^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1*x3^3*x4^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2*x3^2*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2*x3^3*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^2*x3*x4^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^2*x3^3*x4*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^3*x3*x4^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^3*x3^2*x4*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2^2*x3*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^2*x3^3*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^3*x3*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2^3*x3^2*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1*x3^2*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1*x3^3*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1*x4^2*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1*x4^3*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^2*x3*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^2*x4*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^2*x3^3*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^2*x4^3*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^3*x3*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^3*x4*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^3*x3^2*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^3*x4^2*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1*x4^2*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1*x4^3*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2*x3^2*x4^3*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2*x3^3*x4^2*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2*x4^2*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2*x4^3*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^2*x4*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^2*x4^3*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^3*x4*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^3*x4^2*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2^2*x3*x4^3*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^2*x4*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^2*x3^3*x4*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2^2*x4^3*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^3*x3*x4^2*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2^3*x4*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2^3*x3^2*x4*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^3*x4^2*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2*x3^2*x5^3*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2*x3^3*x5^2*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^2*x3*x5^3*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2^2*x3^3*x5*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2^3*x3*x5^2*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^3*x3^2*x5*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2*x4^2*x5^3*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2*x4^3*x5^2*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x3*x4^2*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x3*x4^3*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2^2*x4*x5^3*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^2*x4^3*x5*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^3*x4*x5^2*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2^3*x4^2*x5*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x3^2*x4*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x3^2*x4^3*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x3^3*x4*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x3^3*x4^2*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x3*x4^2*x5^3*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x3*x4^3*x5^2*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x3^2*x4*x5^3*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x3^2*x4^3*x5*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x3^3*x4*x5^2*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x3^3*x4^2*x5*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15)))/((x1 - x2)*(x1 - x3)*(x1 - x4)*(x2 - x3)*(x1 - x5)*(x2 - x4)*(x2 - x5)*(x3 - x4)*(x3 - x5)*(x4 - x5))

[Rex Mantiri]

Let's try with your previous example:

format long g
x = sym('x', [1 15], 'real')

x = 

Potcap = [0.986702168; 0.97272091; 0.957930961; 0.942424001; 0.926404439; 0.909375829; 0.891635315; 0.873329497; 0.854253377; 0.834442537; 0.813592045; 0.791234153; 0.768357994; 0.744306568; 0.719094568; 0.692488019; 0.66411648; 0.634292184; 0.602498593; 0.569711546; 0.534931653];
t = [1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20;21];
x0 = [0.2;0.21;0.22;0.23;0.24;0.31;0.32;0.33;0.34;0.1;0.1;0.1;0.1;0.1;0.3];
N = length(x0);
A = zeros(4,N);
A(1,1) = 1; A(2,2) = 1; A(3,3) = 1; A(4,4) = 1;
A(1,2) = -1; A(2,3) = -1; A(3,4) = -1; A(4,5) = -1;
b(1:4,1) = -eps(realmin);
lb = zeros(15,1); lb(1:9) = eps(realmin)^(1/5);
ub = [Inf Inf Inf Inf Inf Inf Inf Inf Inf 1 1 1 1 1 Inf];
fnc = @(x) Fungsi(x,t,Potcap);
options = optimoptions(@fmincon);
options.MaxFunctionEvaluations = 1e4;
[p, fval, exitflag, output] = fmincon(fnc, x0, A, b, [], [], lb, ub, @mycon, options);

Error using *
Incorrect dimensions for matrix multiplication. Check that the number of columns in the first matrix matches the number of rows in the second matrix. To perform elementwise multiplication, use '.*'.

Error in solution>Fungsi (line 22)
f = sum(((x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)) + x(11)*exp(-(t.*log(x(2)*x(15) + 1))/x(15)) + x(12)*exp(-(t.*log(x(3)*x(15) + 1))/x(15)) + x(13)*exp(-(t.*log(x(4)*x(15) + 1))/x(15)) + x(14)*exp(-(t.*log(x(5)*x(15) + 1))/x(15)) + (x(13)*exp(-(t.*log(x(4)*x(15) + 1))/x(15))*exp(-(t.*log(x(5)*x(15) + 1))/x(15))*(x(9)*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(9)*exp((t.*log(x(5)*x(15) + 1))/x(15))))/(x(4) - x(5)) + (x(6)*x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(exp((t.*log(x(1)*x(15) + 1))/x(15)) - exp((t.*log(x(2)*x(15) + 1))/x(15))))/(x(1) - x(2)) + (x(7)*x(11)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(exp((t.*log(x(2)*x(15) + 1))/x(15)) - exp((t.*log(x(3)*x(15) + 1))/x(15))))/(x(2) - x(3)) + (x(8)*x(12)*exp(-(t.*log(x(3)*x(15) + 1))/x(15))*exp(-(t.*log(x(4)*x(15) + 1))/x(15))*(exp((t.*log(x(3)*x(15) + 1))/x(15)) - exp((t.*log(x(4)*x(15) + 1))/x(15))))/(x(3) - x(4)) + (x(12)*exp(-(t.*log(x(3)*x(15) + 1))/x(15))*exp(-(t.*log(x(4)*x(15) + 1))/x(15))*exp(-(t.*log(x(5)*x(15) + 1))/x(15))*(x(3)*x(8)*x(9)*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(3)*x(8)*x(9)*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(4)*x(8)*x(9)*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(4)*x(8)*x(9)*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(5)*x(8)*x(9)*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(5)*x(8)*x(9)*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15))))/((x(3) - x(4))*(x(3) - x(5))*(x(4) - x(5))) + (x(6)*x(7)*x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(1)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15)) - x(1)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15)) - x(2)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15)) + x(2)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15)) + x(3)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15)) - x(3)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))))/((x(1) - x(2))*(x(1) - x(3))*(x(2) - x(3))) + (x(7)*x(8)*x(11)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*exp(-(t.*log(x(3)*x(15) + 1))/x(15))*exp(-(t.*log(x(4)*x(15) + 1))/x(15))*(x(2)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15)) - x(2)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(3)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15)) + x(3)*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(4)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(4)*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))))/((x(2) - x(3))*(x(2) - x(4))*(x(3) - x(4))) - (x(11)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*exp(-(t.*log(x(3)*x(15) + 1))/x(15))*exp(-(t.*log(x(4)*x(15) + 1))/x(15))*exp(-(t.*log(x(5)*x(15) + 1))/x(15))*(x(2)*x(3)^2*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(2)^2*x(3)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(2)*x(3)^2*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)*x(4)^2*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(2)^2*x(3)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^2*x(4)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(3)*x(4)^2*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(3)^2*x(4)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(2)*x(4)^2*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)*x(5)^2*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)^2*x(4)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)^2*x(5)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)*x(5)^2*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(3)*x(5)^2*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^2*x(5)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(3)^2*x(5)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(3)*x(4)^2*x(7)*x(8)*x(9)*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(3)^2*x(4)*x(7)*x(8)*x(9)*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(3)*x(5)^2*x(7)*x(8)*x(9)*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(4)*x(5)^2*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(3)^2*x(5)*x(7)*x(8)*x(9)*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(4)^2*x(5)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(4)*x(5)^2*x(7)*x(8)*x(9)*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(4)^2*x(5)*x(7)*x(8)*x(9)*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15))))/((x(2) - x(3))*(x(2) - x(4))*(x(2) - x(5))*(x(3) - x(4))*(x(3) - x(5))*(x(4) - x(5))) - (x(6)*x(7)*x(8)*x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*exp(-(t.*log(x(3)*x(15) + 1))/x(15))*exp(-(t.*log(x(4)*x(15) + 1))/x(15))*(x(1)*x(2)^2*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15)) - x(1)^2*x(2)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15)) - x(1)*x(2)^2*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)*x(3)^2*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15)) + x(1)^2*x(2)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(1)^2*x(3)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15)) + x(2)*x(3)^2*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15)) - x(2)^2*x(3)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15)) + x(1)*x(3)^2*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(1)*x(4)^2*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)^2*x(3)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)^2*x(4)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)*x(4)^2*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(2)*x(4)^2*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(1)^2*x(4)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(2)^2*x(4)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(2)*x(3)^2*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(2)^2*x(3)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(2)*x(4)^2*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(3)*x(4)^2*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(2)^2*x(4)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(3)^2*x(4)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(3)*x(4)^2*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(3)^2*x(4)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))))/((x(1) - x(2))*(x(1) - x(3))*(x(1) - x(4))*(x(2) - x(3))*(x(2) - x(4))*(x(3) - x(4))) - (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*exp(-(t.*log(x(3)*x(15) + 1))/x(15))*exp(-(t.*log(x(4)*x(15) + 1))/x(15))*exp(-(t.*log(x(5)*x(15) + 1))/x(15))*(x(1)*x(2)^2*x(3)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)*x(2)^3*x(3)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)^2*x(2)*x(3)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(1)^2*x(2)^3*x(3)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(1)^3*x(2)*x(3)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)^3*x(2)^2*x(3)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)*x(2)^2*x(3)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)*x(2)^2*x(4)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(1)*x(2)^3*x(3)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)*x(2)^3*x(4)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(1)^2*x(2)*x(3)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^2*x(2)*x(4)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)^2*x(2)^3*x(3)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^2*x(2)^3*x(4)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)^3*x(2)*x(3)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^3*x(2)*x(4)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(1)^3*x(2)^2*x(3)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^3*x(2)^2*x(4)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(1)*x(3)^2*x(4)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)*x(3)^3*x(4)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)^2*x(3)*x(4)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(1)^2*x(3)^3*x(4)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(1)^3*x(3)*x(4)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)^3*x(3)^2*x(4)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(1)*x(2)^2*x(4)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)*x(2)^2*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)*x(2)^3*x(4)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)*x(2)^3*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)*x(3)^2*x(4)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(2)*x(3)^3*x(4)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)^2*x(2)*x(4)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^2*x(2)*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^2*x(2)^3*x(4)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^2*x(2)^3*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^3*x(2)*x(4)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^3*x(2)*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^3*x(2)^2*x(4)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^3*x(2)^2*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^2*x(3)*x(4)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(2)^2*x(3)^3*x(4)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(2)^3*x(3)*x(4)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(2)^3*x(3)^2*x(4)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)*x(2)^2*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)*x(2)^3*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)*x(3)^2*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)*x(3)^3*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^2*x(2)*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^2*x(3)*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^2*x(2)^3*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^2*x(3)^3*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^3*x(2)*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^3*x(3)*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^3*x(2)^2*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^3*x(3)^2*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)*x(3)^2*x(4)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)*x(3)^3*x(4)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)*x(3)^2*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)*x(3)^3*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^2*x(3)*x(4)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^2*x(3)^3*x(4)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^3*x(3)*x(4)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^3*x(3)^2*x(4)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)^2*x(3)*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^2*x(3)^3*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^3*x(3)*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)^3*x(3)^2*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)*x(3)^2*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)*x(3)^3*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)*x(4)^2*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)*x(4)^3*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^2*x(3)*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^2*x(4)*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^2*x(3)^3*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^2*x(4)^3*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^3*x(3)*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^3*x(4)*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^3*x(3)^2*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^3*x(4)^2*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)*x(4)^2*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)*x(4)^3*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)*x(3)^2*x(4)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)*x(3)^3*x(4)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)*x(4)^2*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)*x(4)^3*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^2*x(4)*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^2*x(4)^3*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^3*x(4)*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^3*x(4)^2*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)^2*x(3)*x(4)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^2*x(4)*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^2*x(3)^3*x(4)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)^2*x(4)^3*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^3*x(3)*x(4)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)^3*x(4)*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)^3*x(3)^2*x(4)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^3*x(4)^2*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)*x(3)^2*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)*x(3)^3*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^2*x(3)*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)^2*x(3)^3*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)^3*x(3)*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^3*x(3)^2*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)*x(4)^2*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)*x(4)^3*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(3)*x(4)^2*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(3)*x(4)^3*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)^2*x(4)*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^2*x(4)^3*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^3*x(4)*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)^3*x(4)^2*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(3)^2*x(4)*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(3)^2*x(4)^3*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(3)^3*x(4)*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(3)^3*x(4)^2*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(3)*x(4)^2*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(3)*x(4)^3*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(3)^2*x(4)*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(3)^2*x(4)^3*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(3)^3*x(4)*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(3)^3*x(4)^2*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15))))/((x(1) - x(2))*(x(1) - x(3))*(x(1) - x(4))*(x(2) - x(3))*(x(1) - x(5))*(x(2) - x(4))*(x(2) - x(5))*(x(3) - x(4))*(x(3) - x(5))*(x(4) - x(5))))-Potcap).^2)

Error in solution (line 13)
fnc = @(x) Fungsi(x,t,Potcap);

Error in fmincon (line 568)
initVals.f = feval(funfcn{3},X,varargin{:});

Caused by:
Failure in initial objective function evaluation. FMINCON cannot continue.

disp(p)
disp(fval)
disp(exitflag)
disp(output)
function f = Fungsi(x, t, Potcap)
   f = sum(((x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15)) + x(11)*exp(-(t.*log(x(2)*x(15) + 1))/x(15)) + x(12)*exp(-(t.*log(x(3)*x(15) + 1))/x(15)) + x(13)*exp(-(t.*log(x(4)*x(15) + 1))/x(15)) + x(14)*exp(-(t.*log(x(5)*x(15) + 1))/x(15)) + (x(13)*exp(-(t.*log(x(4)*x(15) + 1))/x(15))*exp(-(t.*log(x(5)*x(15) + 1))/x(15))*(x(9)*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(9)*exp((t.*log(x(5)*x(15) + 1))/x(15))))/(x(4) - x(5)) + (x(6)*x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*(exp((t.*log(x(1)*x(15) + 1))/x(15)) - exp((t.*log(x(2)*x(15) + 1))/x(15))))/(x(1) - x(2)) + (x(7)*x(11)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(exp((t.*log(x(2)*x(15) + 1))/x(15)) - exp((t.*log(x(3)*x(15) + 1))/x(15))))/(x(2) - x(3)) + (x(8)*x(12)*exp(-(t.*log(x(3)*x(15) + 1))/x(15))*exp(-(t.*log(x(4)*x(15) + 1))/x(15))*(exp((t.*log(x(3)*x(15) + 1))/x(15)) - exp((t.*log(x(4)*x(15) + 1))/x(15))))/(x(3) - x(4)) + (x(12)*exp(-(t.*log(x(3)*x(15) + 1))/x(15))*exp(-(t.*log(x(4)*x(15) + 1))/x(15))*exp(-(t.*log(x(5)*x(15) + 1))/x(15))*(x(3)*x(8)*x(9)*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(3)*x(8)*x(9)*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(4)*x(8)*x(9)*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(4)*x(8)*x(9)*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(5)*x(8)*x(9)*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(5)*x(8)*x(9)*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15))))/((x(3) - x(4))*(x(3) - x(5))*(x(4) - x(5))) + (x(6)*x(7)*x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*exp(-(t.*log(x(3)*x(15) + 1))/x(15))*(x(1)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15)) - x(1)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15)) - x(2)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15)) + x(2)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15)) + x(3)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15)) - x(3)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))))/((x(1) - x(2))*(x(1) - x(3))*(x(2) - x(3))) + (x(7)*x(8)*x(11)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*exp(-(t.*log(x(3)*x(15) + 1))/x(15))*exp(-(t.*log(x(4)*x(15) + 1))/x(15))*(x(2)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15)) - x(2)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(3)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15)) + x(3)*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(4)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(4)*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))))/((x(2) - x(3))*(x(2) - x(4))*(x(3) - x(4))) - (x(11)*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*exp(-(t.*log(x(3)*x(15) + 1))/x(15))*exp(-(t.*log(x(4)*x(15) + 1))/x(15))*exp(-(t.*log(x(5)*x(15) + 1))/x(15))*(x(2)*x(3)^2*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(2)^2*x(3)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(2)*x(3)^2*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)*x(4)^2*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(2)^2*x(3)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^2*x(4)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(3)*x(4)^2*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(3)^2*x(4)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(2)*x(4)^2*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)*x(5)^2*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)^2*x(4)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)^2*x(5)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)*x(5)^2*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(3)*x(5)^2*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^2*x(5)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(3)^2*x(5)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(3)*x(4)^2*x(7)*x(8)*x(9)*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(3)^2*x(4)*x(7)*x(8)*x(9)*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(3)*x(5)^2*x(7)*x(8)*x(9)*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(4)*x(5)^2*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(3)^2*x(5)*x(7)*x(8)*x(9)*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(4)^2*x(5)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(4)*x(5)^2*x(7)*x(8)*x(9)*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(4)^2*x(5)*x(7)*x(8)*x(9)*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15))))/((x(2) - x(3))*(x(2) - x(4))*(x(2) - x(5))*(x(3) - x(4))*(x(3) - x(5))*(x(4) - x(5))) - (x(6)*x(7)*x(8)*x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*exp(-(t.*log(x(3)*x(15) + 1))/x(15))*exp(-(t.*log(x(4)*x(15) + 1))/x(15))*(x(1)*x(2)^2*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15)) - x(1)^2*x(2)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15)) - x(1)*x(2)^2*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)*x(3)^2*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15)) + x(1)^2*x(2)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(1)^2*x(3)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15)) + x(2)*x(3)^2*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15)) - x(2)^2*x(3)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15)) + x(1)*x(3)^2*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(1)*x(4)^2*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)^2*x(3)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)^2*x(4)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)*x(4)^2*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(2)*x(4)^2*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(1)^2*x(4)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(2)^2*x(4)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(2)*x(3)^2*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(2)^2*x(3)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(2)*x(4)^2*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(3)*x(4)^2*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(2)^2*x(4)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(3)^2*x(4)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(3)*x(4)^2*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(3)^2*x(4)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))))/((x(1) - x(2))*(x(1) - x(3))*(x(1) - x(4))*(x(2) - x(3))*(x(2) - x(4))*(x(3) - x(4))) - (x(10)*exp(-(t.*log(x(1)*x(15) + 1))/x(15))*exp(-(t.*log(x(2)*x(15) + 1))/x(15))*exp(-(t.*log(x(3)*x(15) + 1))/x(15))*exp(-(t.*log(x(4)*x(15) + 1))/x(15))*exp(-(t.*log(x(5)*x(15) + 1))/x(15))*(x(1)*x(2)^2*x(3)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)*x(2)^3*x(3)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)^2*x(2)*x(3)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(1)^2*x(2)^3*x(3)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(1)^3*x(2)*x(3)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)^3*x(2)^2*x(3)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)*x(2)^2*x(3)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)*x(2)^2*x(4)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(1)*x(2)^3*x(3)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)*x(2)^3*x(4)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(1)^2*x(2)*x(3)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^2*x(2)*x(4)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)^2*x(2)^3*x(3)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^2*x(2)^3*x(4)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)^3*x(2)*x(3)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^3*x(2)*x(4)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(1)^3*x(2)^2*x(3)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^3*x(2)^2*x(4)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(1)*x(3)^2*x(4)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)*x(3)^3*x(4)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)^2*x(3)*x(4)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(1)^2*x(3)^3*x(4)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(1)^3*x(3)*x(4)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)^3*x(3)^2*x(4)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(1)*x(2)^2*x(4)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)*x(2)^2*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)*x(2)^3*x(4)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)*x(2)^3*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)*x(3)^2*x(4)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(2)*x(3)^3*x(4)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)^2*x(2)*x(4)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^2*x(2)*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^2*x(2)^3*x(4)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^2*x(2)^3*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^3*x(2)*x(4)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^3*x(2)*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^3*x(2)^2*x(4)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^3*x(2)^2*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^2*x(3)*x(4)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(2)^2*x(3)^3*x(4)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(2)^3*x(3)*x(4)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) + x(2)^3*x(3)^2*x(4)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15)) - x(1)*x(2)^2*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)*x(2)^3*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)*x(3)^2*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)*x(3)^3*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^2*x(2)*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^2*x(3)*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^2*x(2)^3*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^2*x(3)^3*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^3*x(2)*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^3*x(3)*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^3*x(2)^2*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^3*x(3)^2*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)*x(3)^2*x(4)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)*x(3)^3*x(4)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)*x(3)^2*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)*x(3)^3*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^2*x(3)*x(4)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^2*x(3)^3*x(4)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^3*x(3)*x(4)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^3*x(3)^2*x(4)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)^2*x(3)*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^2*x(3)^3*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^3*x(3)*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)^3*x(3)^2*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)*x(3)^2*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)*x(3)^3*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)*x(4)^2*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)*x(4)^3*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^2*x(3)*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^2*x(4)*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^2*x(3)^3*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^2*x(4)^3*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^3*x(3)*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^3*x(4)*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^3*x(3)^2*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^3*x(4)^2*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)*x(4)^2*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)*x(4)^3*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)*x(3)^2*x(4)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)*x(3)^3*x(4)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)*x(4)^2*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)*x(4)^3*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^2*x(4)*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^2*x(4)^3*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(1)^3*x(4)*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(1)^3*x(4)^2*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)^2*x(3)*x(4)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^2*x(4)*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^2*x(3)^3*x(4)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)^2*x(4)^3*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^3*x(3)*x(4)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)^3*x(4)*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)^3*x(3)^2*x(4)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^3*x(4)^2*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)*x(3)^2*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)*x(3)^3*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^2*x(3)*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)^2*x(3)^3*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)^3*x(3)*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^3*x(3)^2*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)*x(4)^2*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)*x(4)^3*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(3)*x(4)^2*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(3)*x(4)^3*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)^2*x(4)*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^2*x(4)^3*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(2)^3*x(4)*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(2)^3*x(4)^2*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(3)^2*x(4)*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(3)^2*x(4)^3*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(3)^3*x(4)*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(3)^3*x(4)^2*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(1)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(3)*x(4)^2*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(3)*x(4)^3*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(3)^2*x(4)*x(5)^3*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(3)^2*x(4)^3*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) - x(3)^3*x(4)*x(5)^2*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15)) + x(3)^3*x(4)^2*x(5)*x(6)*x(7)*x(8)*x(9)*exp((t.*log(x(2)*x(15) + 1))/x(15))*exp((t.*log(x(3)*x(15) + 1))/x(15))*exp((t.*log(x(4)*x(15) + 1))/x(15))*exp((t.*log(x(5)*x(15) + 1))/x(15))))/((x(1) - x(2))*(x(1) - x(3))*(x(1) - x(4))*(x(2) - x(3))*(x(1) - x(5))*(x(2) - x(4))*(x(2) - x(5))*(x(3) - x(4))*(x(3) - x(5))*(x(4) - x(5))))-Potcap).^2)
end
function [c,ceq] = mycon(x)
   c = [];
   ceq = (x(10)+x(11)+x(12)+x(13)+x(14))-1;
end

As you can see there is a problem. Any idea on how to fix it? Thanks.

[Walter Roberson]

The important part of the below is that matlabFunction() will automatically vectorize the expression as it converts it to MATLAB code.

I would have done it once and pasted the result in, but it ended up being over 35 kilobytes, and I would have had to wrap the code onto multiple lines to get it to output.

If you look at the below you will notice that I turned 'optimize', false . I have had problems with the optimization phase in some of the recent versions. You could experiment with turning 'optimize', true and seeing if you get the same results on some random inputs. Oh, wait, you are using R2021a... don't bother with the experiment, the optimizer is broken in R2021a.

format long g
x = sym('x', [1 15], 'real')
x0 = [0.2;0.21;0.22;0.23;0.24;0.31;0.32;0.33;0.34;0.1;0.1;0.1;0.1;0.1;0.3];
N = length(x0);
A = zeros(4,N);
A(1,1) = 1; A(2,2) = 1; A(3,3) = 1; A(4,4) = 1;
A(1,2) = -1; A(2,3) = -1; A(3,4) = -1; A(4,5) = -1;
b(1:4,1) = -eps(realmin);
lb = zeros(15,1); lb(1:9) = eps(realmin)^(1/5);
ub = [Inf Inf Inf Inf Inf Inf Inf Inf Inf 1 1 1 1 1 Inf];

syms(x);  %declare them as individual variables
newPot = x10*exp(-(t*log(x1*x15 + 1))/x15) + x11*exp(-(t*log(x2*x15 + 1))/x15) + x12*exp(-(t*log(x3*x15 + 1))/x15) + x13*exp(-(t*log(x4*x15 + 1))/x15) + x14*exp(-(t*log(x5*x15 + 1))/x15) + (x13*exp(-(t*log(x4*x15 + 1))/x15)*exp(-(t*log(x5*x15 + 1))/x15)*(x9*exp((t*log(x4*x15 + 1))/x15) - x9*exp((t*log(x5*x15 + 1))/x15)))/(x4 - x5) + (x6*x10*exp(-(t*log(x1*x15 + 1))/x15)*exp(-(t*log(x2*x15 + 1))/x15)*(exp((t*log(x1*x15 + 1))/x15) - exp((t*log(x2*x15 + 1))/x15)))/(x1 - x2) + (x7*x11*exp(-(t*log(x2*x15 + 1))/x15)*exp(-(t*log(x3*x15 + 1))/x15)*(exp((t*log(x2*x15 + 1))/x15) - exp((t*log(x3*x15 + 1))/x15)))/(x2 - x3) + (x8*x12*exp(-(t*log(x3*x15 + 1))/x15)*exp(-(t*log(x4*x15 + 1))/x15)*(exp((t*log(x3*x15 + 1))/x15) - exp((t*log(x4*x15 + 1))/x15)))/(x3 - x4) + (x12*exp(-(t*log(x3*x15 + 1))/x15)*exp(-(t*log(x4*x15 + 1))/x15)*exp(-(t*log(x5*x15 + 1))/x15)*(x3*x8*x9*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x3*x8*x9*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x4*x8*x9*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x4*x8*x9*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x5*x8*x9*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x5*x8*x9*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15)))/((x3 - x4)*(x3 - x5)*(x4 - x5)) + (x6*x7*x10*exp(-(t*log(x1*x15 + 1))/x15)*exp(-(t*log(x2*x15 + 1))/x15)*exp(-(t*log(x3*x15 + 1))/x15)*(x1*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15) - x1*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15) - x2*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15) + x2*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15) + x3*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15) - x3*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)))/((x1 - x2)*(x1 - x3)*(x2 - x3)) + (x7*x8*x11*exp(-(t*log(x2*x15 + 1))/x15)*exp(-(t*log(x3*x15 + 1))/x15)*exp(-(t*log(x4*x15 + 1))/x15)*(x2*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15) - x2*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x3*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15) + x3*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x4*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x4*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)))/((x2 - x3)*(x2 - x4)*(x3 - x4)) - (x11*exp(-(t*log(x2*x15 + 1))/x15)*exp(-(t*log(x3*x15 + 1))/x15)*exp(-(t*log(x4*x15 + 1))/x15)*exp(-(t*log(x5*x15 + 1))/x15)*(x2*x3^2*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x2^2*x3*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x2*x3^2*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2*x4^2*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x2^2*x3*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^2*x4*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x3*x4^2*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x3^2*x4*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x2*x4^2*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2*x5^2*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2^2*x4*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2^2*x5*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2*x5^2*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x3*x5^2*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^2*x5*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x3^2*x5*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x3*x4^2*x7*x8*x9*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x3^2*x4*x7*x8*x9*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x3*x5^2*x7*x8*x9*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x4*x5^2*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x3^2*x5*x7*x8*x9*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x4^2*x5*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x4*x5^2*x7*x8*x9*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x4^2*x5*x7*x8*x9*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15)))/((x2 - x3)*(x2 - x4)*(x2 - x5)*(x3 - x4)*(x3 - x5)*(x4 - x5)) - (x6*x7*x8*x10*exp(-(t*log(x1*x15 + 1))/x15)*exp(-(t*log(x2*x15 + 1))/x15)*exp(-(t*log(x3*x15 + 1))/x15)*exp(-(t*log(x4*x15 + 1))/x15)*(x1*x2^2*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15) - x1^2*x2*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15) - x1*x2^2*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1*x3^2*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15) + x1^2*x2*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x1^2*x3*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15) + x2*x3^2*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15) - x2^2*x3*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15) + x1*x3^2*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x1*x4^2*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1^2*x3*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1^2*x4*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1*x4^2*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x2*x4^2*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x1^2*x4*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x2^2*x4*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x2*x3^2*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x2^2*x3*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x2*x4^2*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x3*x4^2*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x2^2*x4*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x3^2*x4*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x3*x4^2*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x3^2*x4*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)))/((x1 - x2)*(x1 - x3)*(x1 - x4)*(x2 - x3)*(x2 - x4)*(x3 - x4)) - (x10*exp(-(t*log(x1*x15 + 1))/x15)*exp(-(t*log(x2*x15 + 1))/x15)*exp(-(t*log(x3*x15 + 1))/x15)*exp(-(t*log(x4*x15 + 1))/x15)*exp(-(t*log(x5*x15 + 1))/x15)*(x1*x2^2*x3^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1*x2^3*x3^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1^2*x2*x3^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x1^2*x2^3*x3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x1^3*x2*x3^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1^3*x2^2*x3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1*x2^2*x3^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1*x2^2*x4^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x1*x2^3*x3^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1*x2^3*x4^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x1^2*x2*x3^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^2*x2*x4^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1^2*x2^3*x3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^2*x2^3*x4*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1^3*x2*x3^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^3*x2*x4^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x1^3*x2^2*x3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^3*x2^2*x4*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x1*x3^2*x4^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1*x3^3*x4^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1^2*x3*x4^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x1^2*x3^3*x4*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x1^3*x3*x4^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1^3*x3^2*x4*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x1*x2^2*x4^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1*x2^2*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1*x2^3*x4^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1*x2^3*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2*x3^2*x4^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x2*x3^3*x4^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1^2*x2*x4^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^2*x2*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^2*x2^3*x4*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^2*x2^3*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^3*x2*x4^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^3*x2*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^3*x2^2*x4*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^3*x2^2*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^2*x3*x4^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x2^2*x3^3*x4*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x2^3*x3*x4^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) + x2^3*x3^2*x4*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15) - x1*x2^2*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1*x2^3*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1*x3^2*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1*x3^3*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^2*x2*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^2*x3*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^2*x2^3*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^2*x3^3*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^3*x2*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^3*x3*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^3*x2^2*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^3*x3^2*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1*x3^2*x4^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1*x3^3*x4^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2*x3^2*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2*x3^3*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^2*x3*x4^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^2*x3^3*x4*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^3*x3*x4^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^3*x3^2*x4*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2^2*x3*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^2*x3^3*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^3*x3*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2^3*x3^2*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1*x3^2*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1*x3^3*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1*x4^2*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1*x4^3*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^2*x3*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^2*x4*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^2*x3^3*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^2*x4^3*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^3*x3*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^3*x4*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^3*x3^2*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^3*x4^2*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1*x4^2*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1*x4^3*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2*x3^2*x4^3*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2*x3^3*x4^2*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2*x4^2*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2*x4^3*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^2*x4*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^2*x4^3*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x1^3*x4*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x1^3*x4^2*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2^2*x3*x4^3*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^2*x4*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^2*x3^3*x4*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2^2*x4^3*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^3*x3*x4^2*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2^3*x4*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2^3*x3^2*x4*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^3*x4^2*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2*x3^2*x5^3*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2*x3^3*x5^2*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^2*x3*x5^3*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2^2*x3^3*x5*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2^3*x3*x5^2*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^3*x3^2*x5*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2*x4^2*x5^3*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2*x4^3*x5^2*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x3*x4^2*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x3*x4^3*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2^2*x4*x5^3*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^2*x4^3*x5*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x2^3*x4*x5^2*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x2^3*x4^2*x5*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x3^2*x4*x5^3*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x3^2*x4^3*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x3^3*x4*x5^2*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x3^3*x4^2*x5*x6*x7*x8*x9*exp((t*log(x1*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x3*x4^2*x5^3*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x3*x4^3*x5^2*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x3^2*x4*x5^3*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x3^2*x4^3*x5*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) - x3^3*x4*x5^2*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15) + x3^3*x4^2*x5*x6*x7*x8*x9*exp((t*log(x2*x15 + 1))/x15)*exp((t*log(x3*x15 + 1))/x15)*exp((t*log(x4*x15 + 1))/x15)*exp((t*log(x5*x15 + 1))/x15)))/((x1 - x2)*(x1 - x3)*(x1 - x4)*(x2 - x3)*(x1 - x5)*(x2 - x4)*(x2 - x5)*(x3 - x4)*(x3 - x5)*(x4 - x5))
syms t Potcap
Fungsi = matlabFunction( sum((newPot-Potcap).^2 ), 'vars', {x, t, Potcap}, 'File', 'Fungsi.m', 'optimize', false);

Potcap_vals = [0.986702168; 0.97272091; 0.957930961; 0.942424001; 0.926404439; 0.909375829; 0.891635315; 0.873329497; 0.854253377; 0.834442537; 0.813592045; 0.791234153; 0.768357994; 0.744306568; 0.719094568; 0.692488019; 0.66411648; 0.634292184; 0.602498593; 0.569711546; 0.534931653];
t_vals = [1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20;21];

fnc = @(x) Fungsi(x, t_vals, Potcap_vals);

options = optimoptions(@fmincon);
options.MaxFunctionEvaluations = 1e4;
[p, fval, exitflag, output] = fmincon(fnc, x0, A, b, [], [], lb, ub, @mycon, options);
disp(p)
disp(fval)
disp(exitflag)
disp(output)

function [c,ceq] = mycon(x)
   c = [];
   ceq = (x(10)+x(11)+x(12)+x(13)+x(14))-1;
end

[Rex Mantiri]

Wow, I never would have guessed that it was a problem with MATLAB. Unfortunately, the code above still doesn't work on my version. It gives the same dimensions do not match error (this time without the little "Incorrect dimensions for matrix multiplication. Check that the number of columns in the first matrix matches the number of rows in the second matrix. To perform elementwise multiplication, use '.*'." part). I have another small question about the fmincon tolerances used in the permutations code. I was thinking that because we are looking at every single case individually, we want the smallest minimum possible for fval. One thing I noticed is that a few perms ended with the Optimality Tolerance condition. Do you think it would be better for me to turn OptimalityTolerance all the way down to get the best results possible? I haven't found any forum posts detailing the effects of basically deleting OptimalityTolerance in fmincon.

[Walter Roberson]

It isn't a problem with MATLAB. You did not vectorize your code. You had terms involving exp(t) * other terms involving exp(t) when those needed to be .* instead of *

For example you have

(x13*exp(-(t*log(x4*x15 + 1))/x15)*exp(-(t*log(x5*x15 + 1))/x15)*(x9*exp((t*log(x4*x15 + 1))/x15)

Notice you have * between the parts you are multiplying. When you converted the named variables to indexed variables, you did not change the * to .*

You can take your existing code that uses () indexing, copy it into a character vector, and vectorize() it, but the result is long.

   f = sum(((x(10).*exp(-(t.*log(x(1).*x(15) + 1))./x(15)) + x(11).*exp( ...
-(t.*log(x(2).*x(15) + 1))./x(15)) + x(12).*exp(-(t.*log(x(3).*x(15) + 1 ...
))./x(15)) + x(13).*exp(-(t.*log(x(4).*x(15) + 1))./x(15)) + x(14).*exp( ...
-(t.*log(x(5).*x(15) + 1))./x(15)) + (x(13).*exp(-(t.*log(x(4).*x(15) +  ...
1))./x(15)).*exp(-(t.*log(x(5).*x(15) + 1))./x(15)).*(x(9).*exp((t.*log( ...
x(4).*x(15) + 1))./x(15)) - x(9).*exp((t.*log(x(5).*x(15) + 1))./x(15))) ...
)./(x(4) - x(5)) + (x(6).*x(10).*exp(-(t.*log(x(1).*x(15) + 1))./x(15)).* ...
exp(-(t.*log(x(2).*x(15) + 1))./x(15)).*(exp((t.*log(x(1).*x(15) + 1))./ ...
x(15)) - exp((t.*log(x(2).*x(15) + 1))./x(15))))./(x(1) - x(2)) + (x(7) ...
.*x(11).*exp(-(t.*log(x(2).*x(15) + 1))./x(15)).*exp(-(t.*log(x(3).*x(15 ...
) + 1))./x(15)).*(exp((t.*log(x(2).*x(15) + 1))./x(15)) - exp((t.*log(x( ...
3).*x(15) + 1))./x(15))))./(x(2) - x(3)) + (x(8).*x(12).*exp(-(t.*log(x( ...
3).*x(15) + 1))./x(15)).*exp(-(t.*log(x(4).*x(15) + 1))./x(15)).*(exp((t ...
.*log(x(3).*x(15) + 1))./x(15)) - exp((t.*log(x(4).*x(15) + 1))./x(15))) ...
)./(x(3) - x(4)) + (x(12).*exp(-(t.*log(x(3).*x(15) + 1))./x(15)).*exp(- ...
(t.*log(x(4).*x(15) + 1))./x(15)).*exp(-(t.*log(x(5).*x(15) + 1))./x(15) ...
).*(x(3).*x(8).*x(9).*exp((t.*log(x(3).*x(15) + 1))./x(15)).*exp((t.*log( ...
x(4).*x(15) + 1))./x(15)) - x(3).*x(8).*x(9).*exp((t.*log(x(3).*x(15) + ...
 1))./x(15)).*exp((t.*log(x(5).*x(15) + 1))./x(15)) - x(4).*x(8).*x(9).* ...
exp((t.*log(x(3).*x(15) + 1))./x(15)).*exp((t.*log(x(4).*x(15) + 1))./x( ...
15)) + x(4).*x(8).*x(9).*exp((t.*log(x(4).*x(15) + 1))./x(15)).*exp((t.* ...
log(x(5).*x(15) + 1))./x(15)) + x(5).*x(8).*x(9).*exp((t.*log(x(3).*x(15 ...
) + 1))./x(15)).*exp((t.*log(x(5).*x(15) + 1))./x(15)) - x(5).*x(8).*x(9 ...
).*exp((t.*log(x(4).*x(15) + 1))./x(15)).*exp((t.*log(x(5).*x(15) + 1))./ ...
x(15))))./((x(3) - x(4)).*(x(3) - x(5)).*(x(4) - x(5))) + (x(6).*x(7).* ...
x(10).*exp(-(t.*log(x(1).*x(15) + 1))./x(15)).*exp(-(t.*log(x(2).*x(15)  ...
+ 1))./x(15)).*exp(-(t.*log(x(3).*x(15) + 1))./x(15)).*(x(1).*exp((t.*log( ...
x(1).*x(15) + 1))./x(15)).*exp((t.*log(x(2).*x(15) + 1))./x(15)) - x(1 ...
).*exp((t.*log(x(1).*x(15) + 1))./x(15)).*exp((t.*log(x(3).*x(15) + 1))./ ...
x(15)) - x(2).*exp((t.*log(x(1).*x(15) + 1))./x(15)).*exp((t.*log(x(2).* ...
x(15) + 1))./x(15)) + x(2).*exp((t.*log(x(2).*x(15) + 1))./x(15)).*exp( ...
(t.*log(x(3).*x(15) + 1))./x(15)) + x(3).*exp((t.*log(x(1).*x(15) + 1))./ ...
x(15)).*exp((t.*log(x(3).*x(15) + 1))./x(15)) - x(3).*exp((t.*log(x(2).* ...
x(15) + 1))./x(15)).*exp((t.*log(x(3).*x(15) + 1))./x(15))))./((x(1) -  ...
x(2)).*(x(1) - x(3)).*(x(2) - x(3))) + (x(7).*x(8).*x(11).*exp(-(t.*log( ...
x(2).*x(15) + 1))./x(15)).*exp(-(t.*log(x(3).*x(15) + 1))./x(15)).*exp(- ...
(t.*log(x(4).*x(15) + 1))./x(15)).*(x(2).*exp((t.*log(x(2).*x(15) + 1))./ ...
x(15)).*exp((t.*log(x(3).*x(15) + 1))./x(15)) - x(2).*exp((t.*log(x(2).* ...
x(15) + 1))./x(15)).*exp((t.*log(x(4).*x(15) + 1))./x(15)) - x(3).*exp( ...
(t.*log(x(2).*x(15) + 1))./x(15)).*exp((t.*log(x(3).*x(15) + 1))./x(15)) ...
 + x(3).*exp((t.*log(x(3).*x(15) + 1))./x(15)).*exp((t.*log(x(4).*x(15)  ...
+ 1))./x(15)) + x(4).*exp((t.*log(x(2).*x(15) + 1))./x(15)).*exp((t.*log ...
(x(4).*x(15) + 1))./x(15)) - x(4).*exp((t.*log(x(3).*x(15) + 1))./x(15)) ...
.*exp((t.*log(x(4).*x(15) + 1))./x(15))))./((x(2) - x(3)).*(x(2) - x(4)) ...
.*(x(3) - x(4))) - (x(11).*exp(-(t.*log(x(2).*x(15) + 1))./x(15)).*exp(- ...
(t.*log(x(3).*x(15) + 1))./x(15)).*exp(-(t.*log(x(4).*x(15) + 1))./x(15) ...
).*exp(-(t.*log(x(5).*x(15) + 1))./x(15)).*(x(2).*x(3).^2.*x(7).*x(8).*x ...
(9).*exp((t.*log(x(2).*x(15) + 1))./x(15)).*exp((t.*log(x(3).*x(15) + 1) ...
)./x(15)).*exp((t.*log(x(4).*x(15) + 1))./x(15)) - x(2).^2.*x(3).*x(7).* ...
x(8).*x(9).*exp((t.*log(x(2).*x(15) + 1))./x(15)).*exp((t.*log(x(3).*x(15 ...
) + 1))./x(15)).*exp((t.*log(x(4).*x(15) + 1))./x(15)) - x(2).*x(3).^2.* ...
x(7).*x(8).*x(9).*exp((t.*log(x(2).*x(15) + 1))./x(15)).*exp((t.*log(x( ...
3).*x(15) + 1))./x(15)).*exp((t.*log(x(5).*x(15) + 1))./x(15)) - x(2).*x ...
(4).^2.*x(7).*x(8).*x(9).*exp((t.*log(x(2).*x(15) + 1))./x(15)).*exp((t ...
.*log(x(3).*x(15) + 1))./x(15)).*exp((t.*log(x(4).*x(15) + 1))./x(15)) +  ...
x(2).^2.*x(3).*x(7).*x(8).*x(9).*exp((t.*log(x(2).*x(15) + 1))./x(15)).* ...
exp((t.*log(x(3).*x(15) + 1))./x(15)).*exp((t.*log(x(5).*x(15) + 1))./x( ...
15)) + x(2).^2.*x(4).*x(7).*x(8).*x(9).*exp((t.*log(x(2).*x(15) + 1))./x ...
(15)).*exp((t.*log(x(3).*x(15) + 1))./x(15)).*exp((t.*log(x(4).*x(15) +  ...
1))./x(15)) + x(3).*x(4).^2.*x(7).*x(8).*x(9).*exp((t.*log(x(2).*x(15) + ...
 1))./x(15)).*exp((t.*log(x(3).*x(15) + 1))./x(15)).*exp((t.*log(x(4).*x ...
(15) + 1))./x(15)) - x(3).^2.*x(4).*x(7).*x(8).*x(9).*exp((t.*log(x(2).* ...
x(15) + 1))./x(15)).*exp((t.*log(x(3).*x(15) + 1))./x(15)).*exp((t.*log( ...
x(4).*x(15) + 1))./x(15)) + x(2).*x(4).^2.*x(7).*x(8).*x(9).*exp((t.*log ...
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15)) + x(1).^3.*x(4).^2.*x(5).*x(6).*x(7).*x(8).*x(9).*exp((t.*log(x(1).* ...
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x(8).*x(9).*exp((t.*log(x(2).*x(15) + 1))./x(15)).*exp((t.*log(x(3).*x( ...
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.*exp((t.*log(x(2).*x(15) + 1))./x(15)).*exp((t.*log(x(3).*x(15) + 1))./ ...
x(15)).*exp((t.*log(x(4).*x(15) + 1))./x(15)).*exp((t.*log(x(5).*x(15) + ...
 1))./x(15)) + x(3).^3.*x(4).^2.*x(5).*x(6).*x(7).*x(8).*x(9).*exp((t.* ...
log(x(2).*x(15) + 1))./x(15)).*exp((t.*log(x(3).*x(15) + 1))./x(15)).*exp ...
((t.*log(x(4).*x(15) + 1))./x(15)).*exp((t.*log(x(5).*x(15) + 1))./x(15) ...
)))./((x(1) - x(2)).*(x(1) - x(3)).*(x(1) - x(4)).*(x(2) - x(3)).*(x(1)  ...
- x(5)).*(x(2) - x(4)).*(x(2) - x(5)).*(x(3) - x(4)).*(x(3) - x(5)).*(x( ...
4) - x(5))))-Potcap).^2)                                                 ...

[Rex Mantiri]

Oh so basically every * and / operation needs to be element-wise huh? That's an easy fix. What about my OptimalityTolerance question above? That is basically the last step and we'll be in the clear. Or should I consider using a different algorithm from the normal interior-point? The results I get are still relatively large here.

[Walter Roberson]

https://www.mathworks.com/help/optim/ug/tolerances-and-stopping-criteria.html

[Rex Mantiri]

Are the other algorithms like

• 'sqp'
• 'sqp-legacy'
• 'active-set'

more accurate or should I stick to interior-point for this problem and just adjust the OptimalityTolerance? I tried with 1e-10 for OptimalityTolerance and it took way too long, so now I am trying with 1e-8. I was just wondering if I can also change the algorithm for accuracy. I'm okay with it taking around 24 hours for the result to come out more accurately. I also read that Medium-scale algorithms might offer better performance but I don't know which algorithm will improve the fit for this problem.

[Walter Roberson]

https://www.mathworks.com/help/optim/ug/choosing-the-algorithm.html

https://www.mathworks.com/help/optim/ug/constrained-nonlinear-optimization-algorithms.html

"SQP methods represent the state of the art in nonlinear programming methods. Schittkowski [36], for example, has implemented and tested a version that outperforms every other tested method in terms of efficiency, accuracy, and percentage of successful solutions, over a large number of test problems. "

[Rex Mantiri]

Alright, I'll give SQP a try. Thanks for all the help, Walter. I've accepted your answer. You have earned your spot in my research acknowledgements haha. Wish you all the best, Walter!

[Rex Mantiri]

After giving SQP a try it ran for only 30 seconds and gave me very satisfactory estimation results. Amazing. Thanks again Walter, my research wouldn't have been possible without your help.

[Alex Sha]

The results below will be better, with the objective function value of 0.000142097015164559

x1	0.552962927693926
x2	7.0900791512254E-10
x3	79.4908429668269
x4	75.943703855999
x5	67.2161454152123
x6	21.3367020418602
x7	5.57437809140671
x8	399.606836671397
x9	38.5601160433331
x10	0.246017494458757
x11	0.00224637052140115
x12	0.122818175986558
x13	0.553876775143463
x14	0.0750411838898768
x15	1055.99540182052

[Walter Roberson]

Thanks, @Alex Sha