How could you modify this semi-infinite optimization to global optimization using GlobalSearch?

Hello

I managed to create a script and find local minimum for my problem based on this example:

https://www.mathworks.com/help/optim/ug/one-dimensional-semi-infinite-constraints.html

But how could you modify that example into a form that uses GlobalSearch to find global minimum? Let's say you have the myfun.m and mycon.m files. Normally you just set x0 and call fseminf and you have a local minimum. I suppose you need to do something like what is written in the answer here:

https://www.mathworks.com/matlabcentral/answers/362625-what-function-can-i-use-for-finding-global-optima-in-semi-infinite-constraint-optimization-problem?s_tid=answers_rc1-1_p1_MLT

So let's say you do this : w1=1:100 and w2=1:100. What next? If you could show me how to modify this MathWorks example, then I could modify my scripts.

Thanks

[Richárd Tóth]

or is it easier if I simply call fseminf lots of times with different values? Is my code going to be as efficient and fast as by using GA,GlobalSearch or some other solver?

Answer 1

[Matt J]

If you could show me how to modify this MathWorks example, then I could modify my scripts.

It would look like below,

myfun=@(x) norm(x-0.5).^2;

[w1,w2]=deal(1:100);

x0=ga(myfun,3,A,b,Aeq,beq,lb,ub,@(x) nonlcon(x,w1,w2));

function [c,ceq]=nonlcon(X,w1,w2)

  K1 = sin(w1*X(1)).*cos(w1*X(2)) - 1/1000*(w1-50).^2 -...
       sin(w1*X(3))-X(3)-1;
   
  K2 = sin(w2*X(2)).*cos(w2*X(1)) - 1/1000*(w2-50).^2 -...
       sin(w2*X(3))-X(3)-1;


 c=[K1;K2];  
 ceq=[];


end

Then, you feed the x0, returned from ga(), as the initial guess to fseminf, exactly as implemented at

https://www.mathworks.com/help/optim/ug/one-dimensional-semi-infinite-constraints.html