I have problem with fmincon

Hello, i need to solve this with optimization toolbox.

My first attempt was this code but this is not optimization toolbox.

clearvars; clc; clear; close all;
%%
n=0;    % initial n
nopt = double(u(n));    % converts symbolic variable to double variable
%%  while loop
while nopt < 49.5
    n=n+1;
    nopt = double(u(n));
end
%%  display results
fprintf('Minimum harmonies should be selected is %d for contain %s of the modulated signal power.\n',n,'%99');
fprintf('Also, with this harmonies we can contain up to %s%.2f of the modulated signal power.\n','%',nopt*2);
%%  function we want to solve
function U = u(x)
    syms k;
    B = symsum((besselj(k,5)).^2,k,1,x);
    A = (besselj(0,5))^2;
    U = 50*(A+2.*B);
end

And i tried with fmincon but i have some errors.

clearvars; clc; clear; close all;
%%
options = optimoptions("fmincon",...
    "Algorithm","interior-point",...
    "EnableFeasibilityMode",true,...
    "SubproblemAlgorithm","cg");
%%
x0=0;
s = fmincon(@objfun,x0,[],[],[],[],[],[],@confun,options);
%%
function f = objfun(x)
    A = (besselj(0,5))^2;
    syms k;
    B = symsum((besselj(k,5)).^2,k,1,x);
    %B = 0.0;
    %for k=1:1:x
    %    B = B + besselj(k,5).^2;
    %end
	F = 50.*(A+2.*B);
	f = matlabFunction(F);
end
%%
function [c,ceq] = confun(x)
	c = 49.5 - objfun(x);
	%c = matlabFunction(C);
	ceq=[];
end

with these errors:

Operator '-' is not supported for operands of type 'function_handle'.

Error in hw2v2>confun (line 24)
	c = 49.5 - objfun(x);

Error in fmincon (line 655)
        [ctmp,ceqtmp] = feval(confcn{3},X,varargin{:});

Error in hw2v2 (line 9)
s = fmincon(@objfun,x0,[],[],[],[],[],[],@confun,options);
 
>> 

Thanks in advance.

Answer 1

[Alan Weiss]

Do not use symbolic variables with Optimization Toolbox functions, unless you convert them to function handles using matlabFunction first. See, for example, Calculate Gradients and Hessians Using Symbolic Math Toolbox™.

You might find it easier to use the Problem-Based Optimization Workflow instead. In that approach, you create symbolic-type optimization variables (NOT using sym or syms, but instead using optimvar).

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation