Regularity Properties of Non-Negative Sparsity Sets

This paper investigates regularity properties of two non-negative sparsity sets: non-negative sparse vectors, and low-rank positive semi-definite matrices. Novel formulae for their Mordukhovich normal cones are given and used to formulate sufficient conditions for non-convex notions of regularity to hold. Our results provide a useful tool for justifying the application of projection methods to certain rank constrained feasibility problems.