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Solving Nonsmooth and Nonconvex Compound Stochastic Programs with Applications to Risk Measure Minimization

Author

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  • Junyi Liu

    (Department of Industrial Engineering, Tsinghua University, Beijing 100084, China)

  • Ying Cui

    (Department of Industrial and Systems Engineering, University of Minnesota, Minneapolis, Minnesota 55455)

  • Jong-Shi Pang

    (Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, California 90089)

Abstract

This paper studies a structured compound stochastic program (SP) involving multiple expectations coupled by nonconvex and nonsmooth functions. We present a successive convex programming-based sampling algorithm and establish its subsequential convergence. We describe stationary properties of the limit points for several classes of the compound SP. We further discuss probabilistic stopping rules based on the computable error bound for the algorithm. We present several risk measure minimization problems that can be formulated as such a compound stochastic program; these include generalized deviation optimization problems based on the optimized certainty equivalent and buffered probability of exceedance (bPOE), a distributionally robust bPOE optimization problem, and a multiclass classification problem employing the cost-sensitive error criteria with bPOE.

Suggested Citation

  • Junyi Liu & Ying Cui & Jong-Shi Pang, 2022. "Solving Nonsmooth and Nonconvex Compound Stochastic Programs with Applications to Risk Measure Minimization," Mathematics of Operations Research, INFORMS, vol. 47(4), pages 3051-3083, November.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:4:p:3051-3083
    DOI: 10.1287/moor.2021.1247
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