Semidefinite programs (SDPs) are convex optimization with vast applications in control theory, quantum information, combinatorial optimization, and operational research. Noisy intermediate-scale (NISQ) algorithms aim to make an efficient use of the current generation hardware. However, optimizing variational is a challenge as it nondeterministic polynomial time-hard problem that general require...

The constraint nondegeneracy condition is one of the most relevant and useful qualifications in nonlinear semidefinite programming. It can be characterized terms any fixed orthonormal basis the, let us say, $$\ell $$ -dimensional kernel matrix, by linear independence a set (\ell +1)/2$$ derivative vectors. We show that this requirement equivalently formulated smaller set, vectors, considering a...