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On Multistage Pseudomonotone Stochastic Variational Inequalities

Author

Listed:
  • Xingbang Cui

    (Tsinghua University)

  • Jie Sun

    (National University of Singapore
    Curtin University)

  • Liping Zhang

    (Tsinghua University)

Abstract

This paper focuses on the solvability of multistage pseudomonotone stochastic variational inequalities (SVIs). On the one hand, some known solvability results of pseudomonotone deterministic variational inequalities cannot be directly extended to multistage pseudomonotone SVIs, so we construct the isomorphism between both and then establish theoretical results on the existence, convexity, boundedness and compactness of the solution set for multistage pseudomonotone SVIs via such an isomorphism. On the other hand, there does not exist a special algorithm for solving the multistage pseudomonotone SVIs so far, so we propose some sufficient conditions on the elicitability of multistage pseudomonotone SVIs, which opens the door for applying Rockafellar’s elicited progressive hedging algorithm to solve such SVIs. Numerical results on solving a two-stage stochastic market optimization problem and randomly generated two-stage pseudomonotone linear complementarity problems are presented.

Suggested Citation

  • Xingbang Cui & Jie Sun & Liping Zhang, 2023. "On Multistage Pseudomonotone Stochastic Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 363-391, October.
    • Handle: RePEc:spr:joptap:v:199:y:2023:i:1:d:10.1007_s10957-023-02289-y
    DOI: 10.1007/s10957-023-02289-y
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    References listed on IDEAS

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    1. 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.
    2. Aswin Kannan & Uday V. Shanbhag, 2019. "Optimal stochastic extragradient schemes for pseudomonotone stochastic variational inequality problems and their variants," Computational Optimization and Applications, Springer, vol. 74(3), pages 779-820, December.
    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.
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