Abstract convexity for nonconvex optimization duality

A. Nedic, A. Ozdaglar, A. Rubinov

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

In this article, we use abstract convexity results to study augmented dual problems for (nonconvex) constrained optimization problems. We consider a nonincreasing function f that is lower semicontinuous at 0 and establish its abstract convexity at 0 with respect to a set of elementary functions defined by nonconvex augmenting functions. We consider three different classes of augmenting functions: nonnegative augmenting functions, bounded-below augmenting functions, and unbounded augmenting functions. We use the abstract convexity results to study augmented optimization duality without imposing boundedness assumptions.

Original languageEnglish (US)
Pages (from-to)655-674
Number of pages20
JournalOptimization
Volume56
Issue number5-6
DOIs
StatePublished - Oct 1 2007
Externally publishedYes

Keywords

  • Abstract convexity
  • Augmenting functions
  • Duality
  • Nonconvex optimization

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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