Is there a mature tool for solving KKT equations in Matlab?

Thanks for reading!

I tried to solve KKT equations by the function "solve" and find it doesn't work when there are multiple solutins. The code is based on https://github.com/sokratisathancsd/kktConditions-Matlab-csdauth

The KKT code is good, so I won't show it. But I find that the solve function which is used there can't show all the multi-solutions, which seems to be the problem of the function solve:

clear;
%%
syms f(x1,x2)
f(x1,x2)=sin(x1).^2+sin(x2).^2;
fx1(x1,x2)=diff(f,x1);
fx2(x1,x2)=diff(f,x2);
g1(x1,x2) = x1;
g2(x1,x2) = -x1+pi*2;
g3(x1,x2) = x2;
g4(x1,x2) = -x2+pi*2;
g=[g1,g2,g3,g4];

%klisi KKT
[x1_sol,x2_sol]=solve([fx1,fx2,g>=0],[x1,x2],'Real',true)

x1_sol = 

x2_sol = 

Clearly, (pi,pi) should also be one of the solutions, so the solution is not enough. In fact, there should be 25 solutions as I can see in the following figure.

If you have any idea why this happens, please refer to this question.

My main question is: what's the better way to calculate KKT equations? Do you have better tools?

Answer 1

[Robert Reed]

Have you tried the MATLAB backslash operator? It does very well for me, even for ill-conditioned problems. I think it uses Cholesky decomposition. There is also a generalized QR decomposition on the File Exchange that is slightly less robust but nevertheless quite good. Robert. A. Reed