Strong duality in optimization: shifted power reformulation. (3rd July 2016)

• Record Type: Journal Article
• Authors: Xia, Yong; Li, Duan
• Is Part Of: Optimization methods and software. Volume 31:Number 4(2016)
• Page Start: 720
• Page End: 736
• Publication Date: 2016-07-03
• Subjects: non-convex optimization -- discrete optimization -- strong duality -- power reformulation; 90C10 -- 90C26 -- 90C46; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2015.1104678
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : For a general class of non-convex optimization problems, a class of power reformulation closes the duality gap between the primal problem and its Lagrangian dual, when the order of the power is sufficiently large. In this paper, we first estimate a lower bound of the power above which the attainment of the zero duality gap can be ensured. After introducing a suitable shifting, we further show, surprisingly, that order three is always sufficient to guarantee the zero duality gap. We then extend the proposed shifted power reformulation to discrete optimization.