A Smoothing Function Approach to Joint Chance-Constrained Programs

Indexed by:Journal Article

Date of Publication:2014-10-01

Journal:JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS

Included Journals:Scopus、SCIE

Volume:163

Issue:1

Page Number:181-199

ISSN:0022-3239

Key Words:Joint chance-constrained programs; Smoothing function; Sequential convex approximation method; DC function

Abstract:In this article, we consider a DC (difference of two convex functions) function approach for solving joint chance-constrained programs (JCCP), which was first established by Hong et al. (Oper Res 59:617-630, 2011). They used a DC function to approximate the probability function and constructed a sequential convex approximation method to solve the approximation problem. However, the DC function they used was nondifferentiable. To alleviate this difficulty, we propose a class of smoothing functions to approximate the joint chance-constraint function, based on which smooth optimization problems are constructed to approximate JCCP. We show that the solutions of a sequence of smoothing approximations converge to a Karush-Kuhn-Tucker point of JCCP under a certain asymptotic regime. To implement the proposed method, four examples in the class of smoothing functions are explored. Moreover, the numerical experiments show that our method is comparable and effective.