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Stochastic golden ratio algorithm to non-convex stochastic mixed variational inequality problem

Author

Listed:
  • Shenghua Wang

    (Hebei Key Laboratory of Physics and Energy Technology, North China Electric Power University)

  • Ziqi Zhu

    (Hebei Key Laboratory of Physics and Energy Technology, North China Electric Power University)

  • Lanxiang Yu

    (Hebei Key Laboratory of Physics and Energy Technology, North China Electric Power University)

Abstract

In [Grad and Lara, J. Optim. Theory Appl. 190(2), 565–580 (2021)], the authors proposed a golden ratio algorithm for solving the deterministic mixed variational inequality problem with prox-convex function. In this paper, we study a new class of stochastic mixed variational inequality problems with the expectation of a prox-convex stochastic function and present a stochastic golden ratio algorithm for solving the proposed problem. The convergence and the convergence rate of our algorithm are shown under some simple and necessary conditions. Finally, we present some numerical examples to illustrate the efficiency of the proposed algorithm.

Suggested Citation

  • Shenghua Wang & Ziqi Zhu & Lanxiang Yu, 2025. "Stochastic golden ratio algorithm to non-convex stochastic mixed variational inequality problem," Journal of Global Optimization, Springer, vol. 91(4), pages 829-850, April.
    • Handle: RePEc:spr:jglopt:v:91:y:2025:i:4:d:10.1007_s10898-024-01445-6
    DOI: 10.1007/s10898-024-01445-6
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    References listed on IDEAS

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    1. Xiao-Juan Zhang & Xue-Wu Du & Zhen-Ping Yang & Gui-Hua Lin, 2019. "An Infeasible Stochastic Approximation and Projection Algorithm for Stochastic Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 1053-1076, December.
    2. Alfredo Iusem & Felipe Lara, 2020. "A Note on “Existence Results for Noncoercive Mixed Variational Inequalities in Finite Dimensional Spaces”," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 607-608, November.
    3. 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.
    4. 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.
    5. Alfredo Iusem & Felipe Lara, 2019. "Existence Results for Noncoercive Mixed Variational Inequalities in Finite Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 122-138, October.
    6. 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.
    7. Sorin-Mihai Grad & Felipe Lara, 2021. "Solving Mixed Variational Inequalities Beyond Convexity," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 565-580, August.
    Full references (including those not matched with items on IDEAS)

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