Hello,
I was trying to use cvx for a SDP optimization problems, My LMIs constraints have some positive definite matrices but i couldn’t find a structure keyword for positive definite.
Note: The LMIs themselves are semidefnite inequalities
How can i get around that?
The documentation on Strict inequalities should be of use here. The bottom line is that CVX can’t help you, you have to help yourself. (To be fair, the solvers can’t help you, either.) You have to decide the best way to handle strict inequalities based on the nature of your model.
For example, choose a small positive number min_eig, to be the smallest allowed eigenvalue. Then positive definiteness with minimum eigenvalue of min_eig or greater for an n by n symmetric matrix A, could be enforced within solver tolerance with the constraint
A - min_eig * eye(n) = semidefinite(n)