Symbolic Optimization

I am trying to optimize a function which gives complex values.

I used fminunc, which gave me vector of complex values though I am giving a vector of real values as the initial guess.

When I used fmincon with FunValCheck property as 'on' it gave an error that problem is in the objective function supplied by the user.

Suggest a method to optimize such a function.

Answer 1

[Sean de Wolski]

Well is the function supposed to give imaginary values? If it's not perhaps you coded the function wrong - we can't help without seeing it.

Else, you could either extract just the real part of the funtion, e.g.:

f = @(x)real(fft(x));

or the absolute value

f = @(x)abs(fft(x));

etc..

[FedRonTev]

The function that I am trying to optimize is:::

f =

(1 - (11^(1/2)*99^(1/2))/330 + (2*R1*(a4*a5 + a6*a8 - 1 - R2*a4*a5*i + R2*i)*i)/(R2*i + R1*R2 + a1*a3 + a2*a7 + a4*a5 + a6*a8 - R1*a4*a5*i - R1*a6*a8*i - R1*R2*a4*a5 - a1*a3*a6*a8 + a1*a4*a6*a7 + a2*a3*a5*a8 - a2*a4*a5*a7 - 1 - R2*a1*a3*i + R1*i - R2*a4*a5*i))^2 + ((11^(1/2)*99^(1/2))/330 - 1 + (2*R1*(a4*a5 + a6*a8 - 1 + R2*a4*a5*i - R2*i)*i)/(R1*R2 - R2*i + a1*a3 + a2*a7 + a4*a5 + a6*a8 + R1*a4*a5*i + R1*a6*a8*i - R1*R2*a4*a5 - a1*a3*a6*a8 + a1*a4*a6*a7 + a2*a3*a5*a8 - a2*a4*a5*a7 - 1 + R2*a1*a3*i - R1*i + R2*a4*a5*i))^2 + (1 + (2*R1*((181*55522^(1/2)*a4*a5)/55522 - (5929741*55522^(1/2))/3082692484 + (181*55522^(1/2)*a6*a8)/55522 - R2*a4*a5*i + (32761*R2*i)/55522)*i)/((32761*R1*R2)/55522 + (5929741*55522^(1/2)*R2*i)/3082692484 + (32761*a1*a3)/55522 + (32761*a2*a7)/55522 + (32761*a4*a5)/55522 + (32761*a6*a8)/55522 - R1*R2*a4*a5 - (181*55522^(1/2)*R1*a4*a5*i)/55522 - (181*55522^(1/2)*R1*a6*a8*i)/55522 - a1*a3*a6*a8 + a1*a4*a6*a7 + a2*a3*a5*a8 - a2*a4*a5*a7 - 1073283121/3082692484 - (181*55522^(1/2)*R2*a1*a3*i)/55522 + (5929741*55522^(1/2)*R1*i)/3082692484 - (181*55522^(1/2)*R2*a4*a5*i)/55522))^2 - (2*R1*((181*55522^(1/2)*a4*a5)/55522 - (5929741*55522^(1/2))/3082692484 + (181*55522^(1/2)*a6*a8)/55522 + R2*a4*a5*i - (32761*R2*i)/55522)*i)/((32761*R1*R2)/55522 - (5929741*55522^(1/2)*R2*i)/3082692484 + (32761*a1*a3)/55522 + (32761*a2*a7)/55522 + (32761*a4*a5)/55522 + (32761*a6*a8)/55522 - R1*R2*a4*a5 + (181*55522^(1/2)*R1*a4*a5*i)/55522 + (181*55522^(1/2)*R1*a6*a8*i)/55522 - a1*a3*a6*a8 + a1*a4*a6*a7 + a2*a3*a5*a8 - a2*a4*a5*a7 - 1073283121/3082692484 + (181*55522^(1/2)*R2*a1*a3*i)/55522 - (5929741*55522^(1/2)*R1*i)/3082692484 + (181*55522^(1/2)*R2*a4*a5*i)/55522) - (4*R1*R2*((32761*a3)/10000 - a3*a6*a8 + a4*a6*a7 - (181*R2*a3*i)/100)^2)/((5929741*R2*i)/1000000 + (32761*R1*R2)/10000 + (32761*a1*a3)/10000 + (32761*a2*a7)/10000 + (32761*a4*a5)/10000 + (32761*a6*a8)/10000 - (181*R1*a4*a5*i)/100 - (181*R1*a6*a8*i)/100 - R1*R2*a4*a5 - a1*a3*a6*a8 + a1*a4*a6*a7 + a2*a3*a5*a8 - a2*a4*a5*a7 - 1073283121/100000000 - (181*R2*a1*a3*i)/100 + (5929741*R1*i)/1000000 - (181*R2*a4*a5*i)/100)^2 + 1 - (2*(R1*R2)^(1/2)*((32761*a3)/10000 - a3*a6*a8 + a4*a6*a7 + (181*R2*a3*i)/100)*i)/((32761*R1*R2)/10000 - (5929741*R2*i)/1000000 + (32761*a1*a3)/10000 + (32761*a2*a7)/10000 + (32761*a4*a5)/10000 + (32761*a6*a8)/10000 + (181*R1*a4*a5*i)/100 + (181*R1*a6*a8*i)/100 - R1*R2*a4*a5 - a1*a3*a6*a8 + a1*a4*a6*a7 + a2*a3*a5*a8 - a2*a4*a5*a7 - 1073283121/100000000 + (181*R2*a1*a3*i)/100 - (5929741*R1*i)/1000000 + (181*R2*a4*a5*i)/100)

The input vector is

[a1 a2 a3 a4 a5 a6 a7 a8 R1 R2]

and initial guess is [.5 .5 .5 .5 .5 .5 .5 .5 1 1].

I want the output vector be scalar and optimised.

[Sean de Wolski]

I'm not an optimization expert, but that function doesn't exactly look at all well posed/stable. I mean 10 dimensions with how many uses of each variable and no constraints? Not to mention - does having an imaginary component double the number of dimensions? (I don't know, but would assume so)

It does have an imaginary component so at least that's correct.

All I can say is good luck!

I wouldn't trust any result you get or any airplane flying with an optimization of that function.

[Sean de Wolski]

Hmm. I guess having an imaginary component wouldn't double the number of dimensions.

Answer 2

[Walter Roberson]

It is an error to use fminbnd() with complex variables or with a function that returns a complex value.

If I recall correctly, the only function that is usable with complex values is the Optimization Toolbox's fgaolattain() -- though perhaps one of the Global Optimization Toolbox's functions could be used.

On the other hand you asked for symbolic optimization in your title; symbolic optimization with complex values is, I believe, available in the symbolic toolbox using MuPad.

[Sean de Wolski]

fgoalattain*