Journal
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
Volume 50, Issue 2, Pages 379-401Publisher
SPRINGER
DOI: 10.1007/s10589-010-9328-4
Keywords
Conditional value-at-risk; Sample average approximation; Smoothing method; Stochastic optimization
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This paper is concerned with solving single CVaR and mixed CVaR minimization problems. A CHKS-type smoothing sample average approximation (SAA) method is proposed for solving these two problems, which retains the convexity and smoothness of the original problem and is easy to implement. For any fixed smoothing constant epsilon, this method produces a sequence whose cluster points are weak stationary points of the CVaR optimization problems with probability one. This framework of combining smoothing technique and SAA scheme can be extended to other smoothing functions as well. Practical numerical examples arising from logistics management are presented to show the usefulness of this method.
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