On Motzkin decomposable sets and functions

M. A. Goberna, J. E. Martínez-Legaz, M. I. Todorov

Research output: Contribution to journalArticleResearchpeer-review

11 Citations (Scopus)

Abstract

A set is called Motzkin decomposable when it can be expressed as the Minkowski sum of a compact convex set with a closed convex cone. The main result in this paper establishes that a closed convex set is Motzkin decomposable if and only if the set of extreme points of its intersection with the linear subspace orthogonal to its lineality is bounded. The paper characterizes the class of the extended functions whose epigraphs are Motzkin decomposable sets showing, in particular, that these functions attain their global minima when they are bounded from below. Calculus of Motzkin decomposable sets and functions is provided. © 2010 Elsevier Inc.
Original languageEnglish
Pages (from-to)525-537
JournalJournal of Mathematical Analysis and Applications
Volume372
DOIs
Publication statusPublished - 1 Dec 2010

Keywords

  • Closed convex sets
  • Convex functions
  • Motzkin decomposition

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