A SEQUENTIAL CONVEX PROGRAM METHOD TO DC PROGRAM WITH JOINT CHANCE CONSTRAINTS

作者:Xiao, Xiantao*; Gu, Jian; Zhang, Liwei; Zhang, Shaowu
来源:Journal of Industrial and Management Optimization, 2012, 8(3): 733-747.
DOI:10.3934/jimo.2012.8.733

摘要

In this paper, we consider a DC (difference of convex) programming problem with joint chance constraints (JCCDCP). We propose a DC function to approximate the constrained function and a corresponding DC program (P epsilon) to approximate the JCCDCP. Under some mild assumptions, we show that the solution of Problem (PE) converges to the solution of JCCDCP when epsilon down arrow 0. A sequential convex program method is constructed to solve the Problem (P epsilon). At each iteration a convex program is solved based on the Monte Carlo method, and the generated optimal sequence is proved to converge to the stationary point of Problem (P epsilon).