Optimization of multiple variables

Hi,

I want to optimize three functions y1,y2,y3,all of them have three variables a1,a2,a3. However, I kept getting errors.Could someone help me?Thx!!!

I try to optimize using fminsearch.

x0=[0 0 0]

result = fminsearch(@optfun,x0);

This is the three functions I want to optimize,and I make them into a vector called optfun(z).

function [y1,y2,y3] = optfun(z)

a1 = z(1);

a2 = z(2);

a3 = z(3);

y1 = abs(vpa("0.122")*a1*sym(1i) + vpa("0.00895")*a2*sym(1i) + vpa("7.32e-4")*a3*sym(1i) + vpa("1530.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("102.0i"))/abs(vpa("0.122")*a1*sym(1i) + vpa("0.00895")*a2*sym(1i) + vpa("7.32e-4")*a3*sym(1i) - vpa("1530.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("102.0i"));

y2 = abs(vpa("0.176")*a1*sym(1i) + vpa("0.0129")*a2*sym(1i) + vpa("0.00106")*a3*sym(1i) - vpa("2200.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("147.0i"))/abs(vpa("0.176")*a1*sym(1i) + vpa("0.0129")*a2*sym(1i) + vpa("0.00106")*a3*sym(1i) + vpa("2200.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("147.0i"));

y3 = abs(vpa("0.223")*a1*sym(1i) + vpa("0.0163")*a2*sym(1i) + vpa("0.00134")*a3*sym(1i) + vpa("2790.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("186.0i"))/abs(vpa("0.223")*a1*sym(1i) + vpa("0.0163")*a2*sym(1i) + vpa("0.00134")*a3*sym(1i) - vpa("2790.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("186.0i"));

end

[Dyuman Joshi]

"However, I kept getting errors."

The code is working fine here.

But, I would suggest to remove the symbolic functions from the code to speed things up.

x0=[0 0 0];
result = fminsearch(@optfun,x0)

result = 1×3

-538.4554 123.5805 140.9954

function [y1,y2,y3] = optfun(z)

a1 = z(1);

a2 = z(2);

a3 = z(3);

y1 = abs(vpa("0.122")*a1*sym(1i) + vpa("0.00895")*a2*sym(1i) + vpa("7.32e-4")*a3*sym(1i) + vpa("1530.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("102.0i"))/abs(vpa("0.122")*a1*sym(1i) + vpa("0.00895")*a2*sym(1i) + vpa("7.32e-4")*a3*sym(1i) - vpa("1530.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("102.0i"));

y2 = abs(vpa("0.176")*a1*sym(1i) + vpa("0.0129")*a2*sym(1i) + vpa("0.00106")*a3*sym(1i) - vpa("2200.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("147.0i"))/abs(vpa("0.176")*a1*sym(1i) + vpa("0.0129")*a2*sym(1i) + vpa("0.00106")*a3*sym(1i) + vpa("2200.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("147.0i"));

y3 = abs(vpa("0.223")*a1*sym(1i) + vpa("0.0163")*a2*sym(1i) + vpa("0.00134")*a3*sym(1i) + vpa("2790.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("186.0i"))/abs(vpa("0.223")*a1*sym(1i) + vpa("0.0163")*a2*sym(1i) + vpa("0.00134")*a3*sym(1i) - vpa("2790.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("186.0i"));

end

[Guan Hao]

Sorry, I didn't state my question clear enough.I mean I want to minimize y1,y2,y3 at the same time.Thx!

[Florian Bidaud]

What do you mean exactly by 'at the same time' ?

You want to minimize the sum of y1, y2 and y3 ? You want to get the minimum possible amongst them ? You want 3 solutions minimizing each y1,y2 and y3 ?

[Stephen23]

Note that FMINSEARCH calls the optimization function with exactly one output argument, so your Y2 and Y3 will be completely ignored. If you do not want them ignored AND you want to use FMINSEARCH then you will need to use some (weighted?) calculation to return exactly one scalar number. No one here call tell you what is the (weighted?) relationship between Y1, Y2, and Y3 that would need to be minimized, only you know that.

[Guan Hao]

@Stephen23

I want to solve y1,y2,y3 as a set of simultaneous equations. a1,a2,a3 should share the same values.

Thus it might be unable to use fminsearch to complete my objective,are there other ways to do that?(Maybe gamultiobj?)

[Stephen23]

"I want to solve y1,y2,y3 as a set of simultaneous equations"

MATLAB already has very efficient tools for solving systems of linear equations:

https://www.mathworks.com/help/matlab/ref/mrdivide.html

https://www.mathworks.com/help/matlab/ref/mldivide.html

It is not clear why you need FMINSEARCH or symbolic variables, I don't think they help you.

[Guan Hao]

The reason I can't change it into equations is that I can't set the equation to a value.

That's ok, cuz I think the weighted output method is a possible way!

Thanks a lot for your help.

Answer 1

[Florian Bidaud]

I assume you want to have three solutions optimizing respectively y1, y2 and y3 ?

In this case you need to split them into 3 functions:

x0=[0 0 0];
result1 = fminsearch(@optfun1,x0)
result2 = fminsearch(@optfun2,x0)
result3 = fminsearch(@optfun3,x0)

function y1 = optfun1(z)
a1 = z(1);
a2 = z(2);
a3 = z(3);
y1 = abs(vpa("0.122")*a1*sym(1i) + vpa("0.00895")*a2*sym(1i) + vpa("7.32e-4")*a3*sym(1i) + vpa("1530.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("102.0i"))/abs(vpa("0.122")*a1*sym(1i) + vpa("0.00895")*a2*sym(1i) + vpa("7.32e-4")*a3*sym(1i) - vpa("1530.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("102.0i"));
end

function y2 = optfun2(z)
a1 = z(1);
a2 = z(2);
a3 = z(3);
y2 = abs(vpa("0.176")*a1*sym(1i) + vpa("0.0129")*a2*sym(1i) + vpa("0.00106")*a3*sym(1i) - vpa("2200.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("147.0i"))/abs(vpa("0.176")*a1*sym(1i) + vpa("0.0129")*a2*sym(1i) + vpa("0.00106")*a3*sym(1i) + vpa("2200.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("147.0i"));
end

function y3 = optfun3(z)
a1 = z(1);
a2 = z(2);
a3 = z(3);
y3 = abs(vpa("0.223")*a1*sym(1i) + vpa("0.0163")*a2*sym(1i) + vpa("0.00134")*a3*sym(1i) + vpa("2790.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("186.0i"))/abs(vpa("0.223")*a1*sym(1i) + vpa("0.0163")*a2*sym(1i) + vpa("0.00134")*a3*sym(1i) - vpa("2790.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("186.0i"));
end

Or maybe you want to minimize the sum of these three functions ?

In this case :

x0=[0 0 0];
result = fminsearch(@optfun,x0)

function y = optfun(z)

a1 = z(1);

a2 = z(2);

a3 = z(3);

y1 = abs(vpa("0.122")*a1*sym(1i) + vpa("0.00895")*a2*sym(1i) + vpa("7.32e-4")*a3*sym(1i) + vpa("1530.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("102.0i"))/abs(vpa("0.122")*a1*sym(1i) + vpa("0.00895")*a2*sym(1i) + vpa("7.32e-4")*a3*sym(1i) - vpa("1530.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("102.0i"));

y2 = abs(vpa("0.176")*a1*sym(1i) + vpa("0.0129")*a2*sym(1i) + vpa("0.00106")*a3*sym(1i) - vpa("2200.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("147.0i"))/abs(vpa("0.176")*a1*sym(1i) + vpa("0.0129")*a2*sym(1i) + vpa("0.00106")*a3*sym(1i) + vpa("2200.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("147.0i"));

y3 = abs(vpa("0.223")*a1*sym(1i) + vpa("0.0163")*a2*sym(1i) + vpa("0.00134")*a3*sym(1i) + vpa("2790.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("186.0i"))/abs(vpa("0.223")*a1*sym(1i) + vpa("0.0163")*a2*sym(1i) + vpa("0.00134")*a3*sym(1i) - vpa("2790.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("186.0i"));

y = y1 + y2 + y3;
end

Maybe you want to do something else, in any case, fminsearch will only minimize the first output, therefore you need to come up with one variable to minimize, or to call it three times

[Guan Hao]

I see...I want to solve y1,y2,y3 as a set of simultaneous equations. a1,a2,a3 should share the same values.

Thus it might be unable to use fminsearch to complete my objective,are there other ways to do that?(Maybe gamultiobj?)

[Florian Bidaud]

Well, technically, since y1, y2 and y3 are positive, if you minimize y1 + y2 + y3, and find a solution for which y1 + y2 + y3 = 0 then you will have y1 = 0, y2 = 0 and y3 = 0, and therefore you will have solve you system.

You can then use :

x0=[0 0 0];
result = fminsearch(@optfun,x0)

function y = optfun(z)

a1 = z(1);

a2 = z(2);

a3 = z(3);

y1 = abs(vpa("0.122")*a1*sym(1i) + vpa("0.00895")*a2*sym(1i) + vpa("7.32e-4")*a3*sym(1i) + vpa("1530.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("102.0i"))/abs(vpa("0.122")*a1*sym(1i) + vpa("0.00895")*a2*sym(1i) + vpa("7.32e-4")*a3*sym(1i) - vpa("1530.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("102.0i"));

y2 = abs(vpa("0.176")*a1*sym(1i) + vpa("0.0129")*a2*sym(1i) + vpa("0.00106")*a3*sym(1i) - vpa("2200.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("147.0i"))/abs(vpa("0.176")*a1*sym(1i) + vpa("0.0129")*a2*sym(1i) + vpa("0.00106")*a3*sym(1i) + vpa("2200.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("147.0i"));

y3 = abs(vpa("0.223")*a1*sym(1i) + vpa("0.0163")*a2*sym(1i) + vpa("0.00134")*a3*sym(1i) + vpa("2790.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("186.0i"))/abs(vpa("0.223")*a1*sym(1i) + vpa("0.0163")*a2*sym(1i) + vpa("0.00134")*a3*sym(1i) - vpa("2790.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("186.0i"));

y = y1 + y2 + y3;
end

However, as Stephen23 said, this is not the best way to solve a system.