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A New Infeasible Projection Method for Stochastic Variational Inequality Problem

Author

Listed:
  • Shenghua Wang

    (North China Electric Power University)

  • Yueyao Zhang

    (North China Electric Power University)

  • Yeol Je Cho

    (Gyeongsang National University
    China Medical University)

Abstract

In this paper, we propose a new infeasible stochastic approximation projection method based on the golden ratio for a nonmonotone stochastic variational inequality problem. In the traditional golden ratio methods, the constant $$\phi $$ ϕ is taken as $$\frac{1+\sqrt{5}}{2}$$ 1 + 5 2 . However, the constant is relaxed to the interval $$(1,\infty )$$ ( 1 , ∞ ) in our method. A new self-adaptive step size which is admitted to be increasing is generated for dealing with the unknown Lipschitz constant of the mapping. The almost sure convergence and convergence rate of the proposed method are shown. Some numerical examples are given to illustrate the competitiveness of our algorithm compared to the related algorithms in the literature. Finally, we apply our method to solve a network bandwidth allocation problem.

Suggested Citation

  • Shenghua Wang & Yueyao Zhang & Yeol Je Cho, 2026. "A New Infeasible Projection Method for Stochastic Variational Inequality Problem," Journal of Optimization Theory and Applications, Springer, vol. 208(1), pages 1-28, January.
    • Handle: RePEc:spr:joptap:v:208:y:2026:i:1:d:10.1007_s10957-025-02825-y
    DOI: 10.1007/s10957-025-02825-y
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    References listed on IDEAS

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    1. Zhen-Ping Yang & Gui-Hua Lin, 2021. "Variance-Based Single-Call Proximal Extragradient Algorithms for Stochastic Mixed Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 393-427, August.
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    5. 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.
    6. Y. Censor & A. Gibali & S. Reich, 2011. "The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 318-335, February.
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