Question about FMINCON in optimization

Question

Haozhe Zhang 2022-10-21

0
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https://ww2.mathworks.cn/matlabcentral/answers/1832593-question-about-fmincon-in-optimization

评论： Haozhe Zhang 2022-10-23

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

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Answer 1

Matt J 2022-10-21

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https://ww2.mathworks.cn/matlabcentral/answers/1832593-question-about-fmincon-in-optimization#answer_1080908

编辑：Matt J 2022-10-22

在 MATLAB Online 中打开

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

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Matt J 2022-10-22

编辑：Matt J 2022-10-22

在 MATLAB Online 中打开

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