Regularity properties of non-negative sparsity sets

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• 作者：Matthew K. Tam ^{m.tam@math.uni-goettingen.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Mordukhovich normal cone ; Regularity ; Sparsity ; Rank constraint ; Positive semi-definite matrices ; Spectral functions
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：447
• 期：2
• 页码：758-777
• 全文大小：470 K

文摘

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.