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Monotonicity and Complexity of Multistage Stochastic Variational Inequalities

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  • Jie Jiang

    (Chongqing University)

  • Hailin Sun

    (Nanjing Normal University)

Abstract

In this paper, we consider multistage stochastic variational inequalities (MSVIs). First, we give multistage stochastic programs and multistage multi-player noncooperative game problems as source problems. After that, we derive the monotonicity properties of MSVIs under less restrictive conditions. Finally, the polynomial rate of convergence with respect to sample sizes between the original problem and its sample average approximation counterpart has been established.

Suggested Citation

  • Jie Jiang & Hailin Sun, 2023. "Monotonicity and Complexity of Multistage Stochastic Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 433-460, February.
    • Handle: RePEc:spr:joptap:v:196:y:2023:i:2:d:10.1007_s10957-022-02099-8
    DOI: 10.1007/s10957-022-02099-8
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    References listed on IDEAS

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    1. Min Li & Chao Zhang, 2020. "Two-Stage Stochastic Variational Inequality Arising from Stochastic Programming," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 324-343, July.
    2. Xiaojun Chen & Masao Fukushima, 2005. "Expected Residual Minimization Method for Stochastic Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 1022-1038, November.
    3. Huifu Xu, 2010. "Sample Average Approximation Methods For A Class Of Stochastic Variational Inequality Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 27(01), pages 103-119.
    4. Jie Jiang & Shengjie Li, 2021. "Regularized Sample Average Approximation Approach for Two-Stage Stochastic Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 650-671, August.
    5. Jie Jiang & Xiaojun Chen & Zhiping Chen, 2020. "Quantitative analysis for a class of two-stage stochastic linear variational inequality problems," Computational Optimization and Applications, Springer, vol. 76(2), pages 431-460, June.
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