Regularity Properties of Non-Negative Sparsity Sets

TL;DR

This paper studies the geometric regularity of non-negative sparsity sets, providing formulas for normal cones and conditions that justify projection methods for rank-constrained problems.

Contribution

It introduces novel formulas for Mordukhovich normal cones of non-negative sparsity sets and establishes conditions for their regularity, aiding projection method applications.

Findings

Formulas for Mordukhovich normal cones of non-negative sparsity sets

Sufficient conditions for regularity properties to hold

Justification for projection methods in rank-constrained problems

Abstract

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.