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

    Access Status
    Fulltext not available
    Authors
    Meng, F.
    Sun, Jie
    Goh, M.
    Date
    2010
    Type
    Journal Article
    
    Metadata
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    Citation
    Meng, F. and Sun, J. and Goh, M. 2010. Stochastic Optimization Problems with CVaR Risk Measure and Their Sample Average Approximation. Journal of Optimization Theory and Applications. 146: pp. 399-418.
    Source Title
    Journal of Optimization Theory and Applications
    DOI
    10.1007/s10957-010-9676-3
    ISSN
    0022-3239
    URI
    http://hdl.handle.net/20.500.11937/37568
    Collection
    • Curtin Research Publications
    Abstract

    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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