Construction of proximal distances over symmetric cones

Julio López, Erik Alex Papa Quiroz

Research output: Contribution to journalArticle

Abstract

© 2017 Informa UK Limited, trading as Taylor & Francis Group. This paper is devoted to the study of proximal distances defined over symmetric cones, which include the non-negative orthant, the second-order cone and the cone of positive semi-definite symmetric matrices. Specifically, our first aim is to provide two ways to build them. For this, we consider two classes of real-valued functions satisfying some assumptions. Then, we show that its corresponding spectrally defined function defines a proximal distance. In addition, we present several examples and some properties of this distance. Taking into account these properties, we analyse the convergence of proximal-type algorithms for solving convex symmetric cone programming (SCP) problems, and we study the asymptotic behaviour of primal central paths associated with a proximal distance. Finally, for linear SCP problems, we provide a relationship between the proximal sequence and the primal central path.
Original languageAmerican English
Pages (from-to)1301-1321
Number of pages21
JournalOptimization
DOIs
StatePublished - 3 Aug 2017

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