Convergence analysis on a smoothing approach to joint chance constrained programs. (1st December 2016)

• Record Type: Journal Article
• Authors: Shan, F.; Xiao, X. T.; Zhang, L. W.
• Is Part Of: Optimization. Volume 65:Number 12(2016)
• Page Start: 2171
• Page End: 2193
• Publication Date: 2016-12-01
• Subjects: Chance constraint -- joint chance constrained programs -- smooth approximation -- convergence analysis; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1233551
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : This paper aims to solve the joint chance constrained programs (JCCP) by a DC (difference of two convex functions) function approach, which was established by Hong et al. [Oper. Res. 2011;59:617–630]. They used a DC function to approximate the chance constraint function and constructed a sequential convex approximation method to solve the approximation problem. A disadvantage of this method is perhaps that the DC function they used is nonsmooth. In this article, we first propose a class of smoothing functions to approximate the maximum function and the indicator function . Then, we construct the conservative smooth DC approximation function to and obtain the smooth DC approximation problems to JCCPs. We show that the solutions of a sequence of smooth approximation problems converge to some Karush–Kuhn–Tucker point of JCCPs under a certain asymptotic regime.