fmincon with nonlcon does not converge to optimum value

function [c ceq] = test_simple(x)
c=[];
ceq=x(1)*x(2);
end
clear;
clc;
fun = @(x) -x(1)^2-x(2)^2
lb = [0;0.2;];
ub = [0.5;0.8];
A = [];
b = [];
Aeq = [];
beq = [];
x0 = [0;0.1];
nonlcon=@test_simple;
options = optimset('MaxFunEvals',Inf,'MaxIter',5000,...
    'Algorithm','interior-point','Display','iter');
[x1, fval1] = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,optimset)

optimum value is 0 0.8 but, matlab execution value is

x1 =
    0.0000
    0.7153

how do i fix it?

[Torsten]

You don't have to pass "optimset" to "fmincon", but "options":

[x1, fval1] = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options)

Best wishes

Torsten.

Answer 1

[Alan Weiss]

The 'interior-point' algorithm cannot allow for points that are right on a boundary, yet your nonlinear constraint attempts to force the points to the boundary. I suggest that you do one of the following:

• Change the lower bound on x(1) to a negative number such as lb = [-0.1;0.2]
• Use the 'sqp' algorithm
• In any case, use a feasible initial point, such as [1e-8;0.3]

Also, after fmincon finishes, try running it again from the final point if the answer isn't reliable (exit flag not equal to 1).

Alan Weiss

MATLAB mathematical toolbox documentation

[YoungChan Kim]

Thank you very much ^^ this answer has helped me a lot

Answer 2

[Walter Roberson]

fmincon is not a global optimizer. You need one of the tools from the Global Optimization Toolbox, such as ga or particleswarm or bounded simulated annealing or patternsearch. (Note: none of those can promise to find the global minima either -- but fmincon doesn't even try.)