Regularity Properties of Non-Negative Sparsity Sets

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.

22 pages

References in corpus (4)

• Alternating Projections and Douglas-Rachford for Sparse Affine Feasibility
• Douglas-Rachford Feasibility Methods for Matrix Completion Problems
• Reflection methods for inverse problems with application to protein conformation determination
• Orbital Geometry in Optimisation

Cited by in corpus (4)

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• Projected gradient descent accumulates at Bouligand stationary points
• Low-Rank Matrix Optimization Over Affine Set
• Method of Alternating Projection for the Absolute Value Equation