Question about FMINCON in optimization

Hi, I got a problem in fmincon in the nonlinear constrained optimization problem. Both target and constrain functions are integral functions. So I named four functions to make it clear.

The function is to optimize a -- a 10x1 array. l is a constant, and x is the variable to be integrated.

The problem is that when I call the fmincon, the function returns an error saying fmincon requires all values returned by functions to be of data type double.

I guess this probablly related to the intefral that I used. But I have no idea how to fix that.

Please help me out, thank you.

clc;clear;
a0 = ones(10,1);
l = 100;
seriesNum = 1;
syms x


% Pass fixed parameters to objfun
objfun3 = @(a)objectiveFcn(l,a);

% Set nondefault solver options
options3 = optimoptions('fmincon','PlotFcn','optimplotfvalconstr');

% Solve
[solution,objectiveValue] = fmincon(objfun3,a0,[],[],[],[],[],[],...
    @constraintFcn,options3);

% Clear variables
clearvars objfun3 options3


% Functions

function f = divsurf(x,l,a,seriesNum)
fi0 = 3;
f = 1/l*(-fi0);
for i = 1:seriesNum
    f = f + a(i)*i*pi/l*cos(i*pi*x/l);
end
f = f^2;
end


function f = surf(x,l,a,seriesNum)
% f = a*(x(2) - x(1)^2)^2 + (1 - x(1))^2;
fi0 = 3;
f = fi0;
for i = 1:seriesNum
    f = f + x / l * (-fi0) + a(i)*sin(i*pi*x/l);
end

end
% The following code creates the objective function. Modify this code for your problem.
function f = objectiveFcn(l,a)
% f = a*(x(2) - x(1)^2)^2 + (1 - x(1))^2;
% l = 100;
syms x
seriesNum = 10;
f = int( @(x)divsurf(x,l,a,seriesNum),x,0,l);
end
% The following code creates the constraint function. Modify this code for your problem.
function [c,ceq] = constraintFcn(a)
lout = 10;
seriesNum = 10;
l = 100;
syms x
% c(1) = x(1)^2 + x(2)^2 - 5;
% c(2) = 3 - x(1)^2 - x(2)^2;
c(1) = int(@(x)surf(x,l,a,seriesNum),x,0,l)-lout;
ceq = [];  % No equality constraints
end

Answer 1

[Matt J]

You shouldn't be using syms, or at least you need to at some point convert your sym expressions as actual numbers. Anything generated by manipulating sym variables will not be a number, e.g.,

syms x

y=int(x.^2,0,1)

y = 

isa(y,'double')

ans = logical
   0

You should probably be integrating numerically, using integral:

y=integral(@(x) x.^2 ,0,1)

y = 0.3333

isa(y,'double')

ans = logical
   1

[Haozhe Zhang]

Thank you. But how to add an integral function (lets say K(a)) as constrain? I tried the numerical integration in K(a)=int(g(x,a),xmin, xmax), but the function for integration has the variable vector (a) that need to be optimized in it. So it is more complicated.

[Matt J]

I don't see anything in your current constraint function that requires Symbolic Math. Why not as follows?

function [c,ceq] = constraintFcn(a)

 lout = 10;
 seriesNum = 10;
 l = 100;

 c = integral(@(x)surf(x,l,a,seriesNum),x,0,l)-lout;
 ceq = [];  % No equality constraints
 
end

[Haozhe Zhang]

Thank you. That works.