Regularity properties of non-negative sparsity sets
Matthew K Tam
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | ACADEMIC PRESS INC ELSEVIER SCIENCE | Published : 2017
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.
Awarded by Deutsche Forschungsgemeinschaft
The author would like to thank Jonathan Borwein and the two anonymous referees for their suggestions. The author is supported by the Deutsche Forschungsgemeinschaft Research Training Grant 2088. The work was partly performed during the author's candidature at the University of Newcastle with the support of an Australian Postgraduate award.