A Smoothing Function Approach to Joint Chance-Constrained Programs

Feng Shan (), Liwei Zhang () and Xiantao Xiao ()
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Feng Shan: Shenyang University of Aeronautics and Astronautics
Liwei Zhang: School of Mathematical Sciences Dalian University of Technology
Xiantao Xiao: School of Mathematical Sciences Dalian University of Technology

Journal of Optimization Theory and Applications, 2014, vol. 163, issue 1, No 9, 199 pages

Abstract: 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.

Keywords: Joint chance-constrained programs; Smoothing function; Sequential convex approximation method; DC function; 90C15; 90C26; 90C30 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10957-013-0513-3

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