Stochastic Optimization Problems with CVaR Risk Measure and Their Sample Average Approximation

被引：0
作者：
F. W. Meng
J. Sun
M. Goh
机构：
[1] National University of Singapore,Logistic Institute—Asia Pacific
[2] National University of Singapore,School of Business and Risk Management Institute
[3] University of South Australia,undefined
来源：
Journal of Optimization Theory and Applications | 2010年 / 146卷
关键词：
Conditional value-at-risk; Sample average approximation; Stochastic optimization; Variational analysis;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We provide a refined convergence analysis for the SAA (sample average approximation) method applied to stochastic optimization problems with either single or mixed CVaR (conditional value-at-risk) measures. Under certain regularity conditions, it is shown that any accumulation point of the weak GKKT (generalized Karush-Kuhn-Tucker) points produced by the SAA method is almost surely a weak stationary point of the original CVaR or mixed CVaR optimization problems. In addition, it is shown that, as the sample size increases, the difference of the optimal values between the SAA problems and the original problem tends to zero with probability approaching one exponentially fast.
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页码：399 / 418
页数：19
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