quadprog output: this problem is non-convex

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Changhe
Changhe 2024-8-14
评论： Walter Roberson 2024-8-14
I am trying to solve a quadratic optimization problem but quadprog keeps telling me that my problem is non-convex.
After several experiments, I found that the problem comes from the equation constraints matrix A, which is a 57250*57441 matrix.
For the following code,
[m, n] = size(A);
assert(m < n);
options = optimoptions('quadprog','Display','off');
[Pwp,fval,exitflag,output] = quadprog(speye(n), zeros(n,1), [], [], A, zeros(m, 1), [], [], [], options);
obviously the solution should be the all-zero vector. But the output still said that this is a nonconvex problem.
=============
Update: I am using matlab 2022b. Here is the link for the mat file of my matrix A:
https://www.dropbox.com/t/eeqMCurgyrgy8brB
I am sorry that it's larger than 5MB so I can only put the link here instead of directly attaching it to this post.
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Walter Roberson
Walter Roberson 2024-8-14
All, I was counting on the fact that there was no error message, and was not checking exitflag . exitflag is showing up as -6, non-convex problem detected.
Walter Roberson
Walter Roberson 2024-8-14
Unfortunately the invoked routine, ipqpsparse, is a .p file, so we cannot examine what is going on internally.

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采纳的回答

Matt J
Matt J 2024-8-14
编辑：Matt J 2024-8-14
I think you probably should report it as a bug, but a possible workaround would be to approximate the original problem with inequality constraints,
b=repelem(1e-10,m);
[Pwp,fval,exitflag,output] = ...
quadprog(speye(n), zeros(n,1), [A;-A], [b;b], [], [], [], [], [], options);

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Torsten
Torsten 2024-8-14
移动：Torsten 2024-8-14
Ran in:
Maybe there are Inf or NaN coefficients in your A ? The following small example works.
A = rand(53,66);
[m,n] = size(A);
options = optimoptions('quadprog','Display','off');
[Pwp,fval,exitflag,output] = quadprog(speye(n), zeros(n,1), [], [], A, zeros(m, 1), [], [], [], options)
Pwp = 66x1
1.0e-13 * -0.0955 -0.1044 -0.0355 0.0400 0.0122 0.1021 -0.0133 0.0133 -0.0910 0.1088
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fval = 3.2638e-27
exitflag = 1
output = struct with fields:
message: 'Minimum found that satisfies the constraints....' algorithm: 'interior-point-convex' firstorderopt: 2.0437e-16 constrviolation: 3.1306e-14 iterations: 1 linearsolver: 'sparse' cgiterations: []
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