Convergence analysis on a smoothing approach to joint chance constrained programs. (1st December 2016) - Shan, F.; Xiao, X. T.; Zhang, L. W.
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.