Asymptotic closure condition and Fenchel duality for DC optimization problems in locally convex spaces

D. H. Fang, C. Li, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

9 Citations (Scopus)

Abstract

We consider the DC optimization problem (P)infx∈X(f1(x)-f2(x))+(g1(Ax)-g2(Ax)), wheref1,f2,g1andg2are proper convex functions defined on locally convex Hausdorff topological vector spaces X and Y respectively, and A is a linear continuous operator from X to Y. Adopting the standard convexification technique, a Fenchel dual problem of (P) is given. By using properties of the epigraph of conjugate functions, some sufficient and necessary conditions for the Fenchel duality and for the stable Fenchel duality of (P) are provided.
Original languageEnglish
Pages (from-to)3672-3681
Number of pages10
JournalNonlinear Analysis, Theory, Methods and Applications
Volume75
Issue number8
DOIs
Publication statusPublished - 1 May 2012

Keywords

  • DC programming
  • Fenchel duality
  • Locally convex space

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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