I want to add a constraint to a convex program, to guarantee some matrix $A$ to be positive semidefinite. How should I do it?
The library I am working with can cope with linear/ quadratic inequalities only.
By definition, $A$ is positive semidefinite iff $\forall x \in \mathbb C^n : x^T A x \geq 0$, but this is a set of inifinitely many constraints. So, my question is: how can I formulate it using a finitely many set of contraints and using linear/ quadratic inequalities only.
Thanks in advance!