Find non-singular solution to equation

[Ed]

Hello,

I have a problem in which one of the constraints is an equality A*X==B, where A and B are known m by n matrices (m<n) and X is a square matrix. Is there a way I can tell YALMIP to look for a non-singular solution X? I am using MOSEK as my solver.

I am currently adding the constraint X+X'>=0 in order to obtain a non-singular X, but I would prefer not to restrict my code to positive solutions only.

Thanks in advance.

[Johan Löfberg]

nonsingular is a horribly nonconvex constraint, and there is no good strategy

X+X'>=0 does not enforce X to be non-singular.

If you want to define X o be positive semidefinite, you have to define X as symmetric (which is default for square matrices) and then add X>=0. To get it positive definite, you add a lower bound, X>=margin*eye(n). Of course, positive definite is a much smaller set than the set of non-singular matrices