A Smoothing Function Approach to Joint Chance-Constrained Programs

作者：Shan, Feng; Zhang, Liwei; Xiao, Xiantao^*

来源：Journal of Optimization Theory and Applications, 2014, 163(1): 181-199.

DOI：10.1007/s10957-013-0513-3

• Joint chance-constrained programs
• Smoothing function
• Sequential convex approximation method
• DC function

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.

• 出版日期2014-10
• 单位大连理工大学; 沈阳航空航天大学