Extended Farkas lemma and strong duality for composite optimization problems with DC functions. (1st February 2017)

• Record Type: Journal Article
• Authors: Fang, Donghui; Gong, Xin
• Is Part Of: Optimization. Volume 66:Number 2(2017)
• Page Start: 179
• Page End: 196
• Publication Date: 2017-02-01
• Subjects: DC optimization problem -- composite function -- strong duality -- Farkas lemma -- conical programming; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1266628
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we consider the optimization problem in locally convex Hausdorff topological vector spaces with objectives given as the difference of two composite functions and constraints described by an arbitrary (possibly infinite) number of convex inequalities. Using the epigraph technique, we introduce some new constraint qualifications, which completely characterize the Farkas lemma, the dualities between the primal problem and its dual problem. Applications to the conical programming with DC composite function are also given.