Stable and total 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

37 Citations (Scopus)

Abstract

We consider the DC (difference of two convex functions) optimization problem (P) inf xεX {(F1(x) - f2((x)) + (g 1((Ax) - g2((Ax))}, where f 1(, f 2(, g1(, and g2( are proper convex functions defined on locally convex Hausdorff topological vector spaces X and Y, and A is a linear continuous operator from X to Y. Adopting different tactics, two types of the Fenchel dual problems of (P) are given. By using the properties of the epigraph of the conjugate functions, some sufficient and necessary conditions for the weak duality of (P) are provided. Sufficient and/or necessary conditions for the strong Fenchel duality, the stable Fenchel duality, and the stable total duality are derived.
Original languageEnglish
Pages (from-to)730-760
Number of pages31
JournalSIAM Journal on Optimization
Volume21
Issue number3
DOIs
Publication statusPublished - 24 Oct 2011

Keywords

  • Difference of two convex functions programming
  • Strong Fenchel duality
  • Total Fenchel duality

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science

Cite this