How to use fminunc for a 2D function composed of two functions?
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I have:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1724231/image.png)
and I want to minimize it on the unit square
without using differentials.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1724236/image.png)
I use the following code,
close all; clear; clc;
options = optimoptions(@fminunc,'Display','iter','Algorithm','quasi-newton');
xy_guess = [0,0];
[xy_opt,fval] = fminunc(@quadratic,xy_guess,options)
function f = quadratic(in)
x = in(1);
y = in(2);
f = -5.*x - 5.*y + 10.*x.^2 + 2.*x.*y
f = 1/200.*(-1000.*x - 1000.*y + 400.*x.*y + 1200.*y.^2 + 5.*cos(30.*x) + 4.*cos(80.*x.^2) + 5.*cos(30.*y) + 4.*cos(80.*y^2))
But declaring f twice does not work. How should I declare this double-function as an input for fminunc ?
Thanks!
2 Commenti
Ashutosh Thakur
il 28 Giu 2024
Hi Sergio,
With the last line of code the value of f is overwritten, and only this value is passed to the fminunc. Also I have observed that you have a constraint on the unit square. You can take advantage of the fmincon function, https://www.mathworks.com/help/optim/ug/fmincon.html, as fminunc does not have any constraint.
Can you try to use fmincon function?
Risposta accettata
Aquatris
il 28 Giu 2024
Modificato: Aquatris
il 28 Giu 2024
You dont seem to have a double function.
So here is a code to solve your problem. You have local minimas so fmincon and brute force approach gives you different results, since brute force approach is a global optimization.
f = @(x) [x(1) x(2)]*[10 2;2 6]*[x(1);x(2)]-[5 5]*[x(1);x(2)]+(cos(30*x(1))+cos(30*x(2)))/40+(cos(80*x(1)^2)+cos(80*x(2)^2))/50;
options = optimoptions(@fmincon);
%options = optimoptions(@fmincon,'Display','iter','OptimalityTolerance',1e-12);
lb = [0 0];% lower bounds
ub = [1 1];% upper bounds
x0 = [.5 .5]; % initial guess
[xSol,fval,exitflag,output] = fmincon(f,x0,[],[],[],[],lb,ub,[],options); % solve optimization
% brute force searching the entire space for min function value
x1 = 0:0.001:1;
x2 = 0:0.001:1;
[X1,X2] = meshgrid(x1,x2);
fValBrute = arrayfun(@(x1,x2)f([x1 x2]),X1,X2);
idxMin = find(fValBrute == min(fValBrute,[],'all')); % find minimum function value
% plot
contourf(X1,X2,fValBrute,150)
hold on
plot(xSol(1),xSol(2),'k*') % black star is the result of fmincon
plot(X1(idxMin),X2(idxMin),'rx') % red x is the brute force result
title({sprintf('Min function value found via fmincon: %.4f at [%.4f %.4f]',fval,xSol(1),xSol(2));
sprintf('Min function value found via brute force: %.4f at [%.4f %.4f]',fValBrute(idxMin),X1(idxMin),X2(idxMin))})
hold off
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