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Dynamic stochastic projection method for multistage stochastic variational inequalities

Author

Listed:
  • Bin Zhou

    (Nanjing Normal University)

  • Jie Jiang

    (Chongqing University)

  • Hailin Sun

    (Nanjing Normal University)

Abstract

Stochastic approximation (SA) type methods have been well studied for solving single-stage stochastic variational inequalities (SVIs). This paper proposes a dynamic stochastic projection method (DSPM) for solving multistage SVIs. In particular, we investigate an inexact single-stage SVI and present an inexact stochastic projection method (ISPM) for solving it. Then we give the DSPM to a three-stage SVI by applying the ISPM to each stage. We show that the DSPM can achieve an $$\mathcal {O}(\frac{1}{\epsilon ^2})$$ O ( 1 ϵ 2 ) convergence rate regarding to the total number of required scenarios for the three-stage SVI. We also extend the DSPM to the multistage SVI when the number of stages is larger than three. The numerical experiments illustrate the effectiveness and efficiency of the DSPM.

Suggested Citation

  • Bin Zhou & Jie Jiang & Hailin Sun, 2024. "Dynamic stochastic projection method for multistage stochastic variational inequalities," Computational Optimization and Applications, Springer, vol. 89(2), pages 485-516, November.
    • Handle: RePEc:spr:coopap:v:89:y:2024:i:2:d:10.1007_s10589-024-00594-4
    DOI: 10.1007/s10589-024-00594-4
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    References listed on IDEAS

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    1. 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.
    2. Woo Chang Kim & Do-Gyun Kwon & Yongjae Lee & Jang Ho Kim & Changle Lin, 2020. "Personalized goal-based investing via multi-stage stochastic goal programming," Quantitative Finance, Taylor & Francis Journals, vol. 20(3), pages 515-526, March.
    3. Hu, Shaolong & Han, Chuanfeng & Dong, Zhijie Sasha & Meng, Lingpeng, 2019. "A multi-stage stochastic programming model for relief distribution considering the state of road network," Transportation Research Part B: Methodological, Elsevier, vol. 123(C), pages 64-87.
    4. 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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