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Variable sample-size optimistic mirror descent algorithm for stochastic mixed variational inequalities

Author

Listed:
  • Zhen-Ping Yang

    (Jiaying University)

  • Yong Zhao

    (Chongqing Jiaotong University)

  • Gui-Hua Lin

    (Shanghai University)

Abstract

In this paper, we propose a variable sample-size optimistic mirror descent algorithm under the Bregman distance for a class of stochastic mixed variational inequalities. Different from those conventional variable sample-size extragradient algorithms to evaluate the expected mapping twice at each iteration, our algorithm requires only one evaluation of the expected mapping and hence can significantly reduce the computation load. In the monotone case, the proposed algorithm can achieve $${\mathcal {O}}(1/t)$$ O ( 1 / t ) ergodic convergence rate in terms of the expected restricted gap function and, under the strongly generalized monotonicity condition, the proposed algorithm has a locally linear convergence rate of the Bregman distance between iterations and solutions when the sample size increases geometrically. Furthermore, we derive some results on stochastic local stability under the generalized monotonicity condition. Numerical experiments indicate that the proposed algorithm compares favorably with some existing methods.

Suggested Citation

  • Zhen-Ping Yang & Yong Zhao & Gui-Hua Lin, 2024. "Variable sample-size optimistic mirror descent algorithm for stochastic mixed variational inequalities," Journal of Global Optimization, Springer, vol. 89(1), pages 143-170, May.
    • Handle: RePEc:spr:jglopt:v:89:y:2024:i:1:d:10.1007_s10898-023-01346-0
    DOI: 10.1007/s10898-023-01346-0
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    References listed on IDEAS

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    1. 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.
    2. Jinlong Lei & Uday V. Shanbhag & Jong-Shi Pang & Suvrajeet Sen, 2020. "On Synchronous, Asynchronous, and Randomized Best-Response Schemes for Stochastic Nash Games," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 157-190, February.
    3. B. Jadamba & F. Raciti, 2015. "Variational Inequality Approach to Stochastic Nash Equilibrium Problems with an Application to Cournot Oligopoly," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 1050-1070, June.
    4. Ahmet Alacaoglu & Yura Malitsky & Volkan Cevher, 2021. "Forward-reflected-backward method with variance reduction," Computational Optimization and Applications, Springer, vol. 80(2), pages 321-346, November.
    5. Xiantao Xiao, 2021. "A Unified Convergence Analysis of Stochastic Bregman Proximal Gradient and Extragradient Methods," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 605-627, March.
    6. Jiří V. Outrata & Jan Valdman, 2020. "On computation of optimal strategies in oligopolistic markets respecting the cost of change," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(3), pages 489-509, December.
    7. repec:inm:orstsy:v:11:y:2021:i:2:p:112-139 is not listed on IDEAS
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