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Stochastic mathematical programs with probabilistic complementarity constraints: SAA and distributionally robust approaches

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  • Shen Peng

    (KTH Royal Institute of Technology)

  • Jie Jiang

    (Chongqing University)

Abstract

In this paper, a class of stochastic mathematical programs with probabilistic complementarity constraints is considered. We first investigate convergence properties of sample average approximation (SAA) approach to the corresponding chance constrained relaxed complementarity problem. Our discussion can be not only applied to the specific model in this paper, but also viewed as a supplementary for the SAA approach to general joint chance constrained problems. Furthermore, considering the uncertainty of the underlying probability distribution, a distributionally robust counterpart with a moment ambiguity set is proposed. The numerically tractable reformulation is derived. Finally, we use a production planing model to report some preliminary numerical results.

Suggested Citation

  • Shen Peng & Jie Jiang, 2021. "Stochastic mathematical programs with probabilistic complementarity constraints: SAA and distributionally robust approaches," Computational Optimization and Applications, Springer, vol. 80(1), pages 153-184, September.
    • Handle: RePEc:spr:coopap:v:80:y:2021:i:1:d:10.1007_s10589-021-00292-5
    DOI: 10.1007/s10589-021-00292-5
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    References listed on IDEAS

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    Cited by:

    1. Jiang, Jie & Peng, Shen, 2024. "Mathematical programs with distributionally robust chance constraints: Statistical robustness, discretization and reformulation," European Journal of Operational Research, Elsevier, vol. 313(2), pages 616-627.

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