Asymptotic Analysis of Sample Average Approximation for Stochastic Optimization Problems with Joint Chance Constraints via Conditional Value at Risk and Difference of Convex Functions

Hailin Sun (), Huifu Xu () and Yong Wang ()
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Hailin Sun: Harbin Institute of Technology
Huifu Xu: University of Southampton
Yong Wang: Harbin Institute of Technology

Journal of Optimization Theory and Applications, 2014, vol. 161, issue 1, No 14, 257-284

Abstract: Abstract Conditional Value at Risk (CVaR) has been recently used to approximate a chance constraint. In this paper, we study the convergence of stationary points, when sample average approximation (SAA) method is applied to a CVaR approximated joint chance constrained stochastic minimization problem. Specifically, we prove under some moderate conditions that optimal solutions and stationary points, obtained from solving sample average approximated problems, converge with probability one to their true counterparts. Moreover, by exploiting the recent results on large deviation of random functions and sensitivity results for generalized equations, we derive exponential rate of convergence of stationary points. The discussion is also extended to the case, when CVaR approximation is replaced by a difference of two convex functions (DC-approximation). Some preliminary numerical test results are reported.

Keywords: Joint chance constraints; CVaR; DC-approximation; Almost H-calmness; Stationary point; Exponential convergence (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10957-012-0127-1

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