Title of Paper:Convergence analysis on a smoothing approach to joint chance constrained programs

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Date of Publication:2016-01-01

Journal:OPTIMIZATION

Included Journals:SCIE、Scopus

Volume:65

Issue:12

Page Number:2171-2193

ISSN No.:0233-1934

Key Words:Chance constraint; joint chance constrained programs; smooth approximation; convergence analysis

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 E [1[0,8)(c(x,.))] and constructed a sequential convex approximation method to solve the approximation problem. A disadvantage of this method is perhaps that the DCfunction they used is nonsmooth. In this article, wefirst propose a class of smoothing functions to approximate the maximum function c(., z) and the indicator function 1[0,8)(.). Then, we construct the conservative smooth DC approximation function to E [1[0,8)(c(x,.))] 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.