How to use Simulated Annealing Algorithm with matrices in the function

I want to find the minimum of the function by Simulated Annealing Algorithm where the function invovles the matrices and FFT also

like this f = Em.*exp(angle(fftshift(ifft2(fftshift(sqrt(v1)*Emmf11a+sqrt(v2)*Emmf11b.*exp(-1i*(v3*pi))));

where Em, Emmf11a, Emmf11b are matrices of 1000x1000 and we have variables as v1, v2 and v3. and conditions are v1 + v2 = 1 and 0=< v3 >=2*pi

or is there any other algorithm that can determine the minimum or the maximum of the function ??

Answer 1

[Alan Weiss]

Optimization Toolbox and Global Optimization Toolbox minimize scalar functions. If your objective function f is a scalar, not a vector or matrix, then the toolbox functions can work.

simulannealbnd works only on bounded problems, so you would have to reformulate your problem from three decision variables to two as follows:

 v2 = 1 - v1

Minimize over v1 and v3. Use the vector x = (v1,v3), a 2-D vector, with bounds

 lb = [-Inf,0];
 ub = [Inf,2*pi];

For details of the syntax for bounds, see the documentation.

Alan Weiss

MATLAB mathematical toolbox documentation

[Liaquat Ali]

if my function is vector then it does not work and from where i can get the file simulannealbnd ??

[Alan Weiss]

simulannealbnd ships with Global Optimization Toolbox. You need a Global Optimization Toolbox license to run this function.

If you have a multiobjective function (you are trying to minimize several values at once) then you can try using gamultiobj, or fgoalattain.

Alan Weiss

MATLAB mathematical toolbox documentation

[Liaquat Ali]

Actually f is not a scalar rather it is a 1000X1000 matrix and i want to find the values of V1, V2 and V3 for which the f is maximum ??

[Alan Weiss]

What does it mean to find the maximum of a matrix? I know what it means to find the maximum of one element in a matrix. However, as soon as you have two or more elements, it can be that changing the V matrix causes one element to increase, another to decrease, and so there is a trade off. Therefore, there is no such thing as the maximum of a function that has two or more elements. There is multiobjective optimization (see my previous link) that explicitly deals with multiple objective functions.

It is possible you want to maximize the sum of squares of the elements of your matrix. In that case, sum the squares as your objective function, and maximize that.

Alan Weiss

MATLAB mathematical toolbox documentation