DC approach to weakly convex optimization and nonconvex quadratic optimization problems. (1st February 2018)

• Record Type: Journal Article
• Authors: Nguyen, Linh T. H.
• Is Part Of: Optimization. Volume 67:Number 2(2018)
• Page Start: 195
• Page End: 216
• Publication Date: 2018-02-01
• Subjects: Difference of convex program -- weakly convex -- nonconvex quadratic problem -- convex polynomial -- robust optimization; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1391251
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: Motivated by weakly convex optimization and quadratic optimization problems, we first show that there is no duality gap between a difference of convex (DC) program over DC constraints and its associated dual problem. We then provide certificates of global optimality for a class of nonconvex optimization problems. As an application, we derive characterizations of robust solutions for uncertain general nonconvex quadratic optimization problems over nonconvex quadratic constraints.