IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v91y2025i4d10.1007_s10898-024-01445-6.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-024-01445-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10898-024-01445-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    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. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sorin-Mihai Grad & Felipe Lara & Raúl Tintaya Marcavillaca, 2024. "Relaxed-Inertial Proximal Point Algorithms for Nonconvex Equilibrium Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 203(3), pages 2233-2262, December.
    2. Sorin-Mihai Grad & Felipe Lara & Raúl T. Marcavillaca, 2025. "Strongly Quasiconvex Functions: What We Know (So Far)," Journal of Optimization Theory and Applications, Springer, vol. 205(2), pages 1-41, May.
    3. A. Iusem & F. Lara, 2022. "Proximal Point Algorithms for Quasiconvex Pseudomonotone Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 443-461, June.
    4. 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.
    5. Alfredo Iusem & Felipe Lara & Raúl T. Marcavillaca & Le Hai Yen, 2024. "A Two-Step Proximal Point Algorithm for Nonconvex Equilibrium Problems with Applications to Fractional Programming," Journal of Global Optimization, Springer, vol. 90(3), pages 755-779, November.
    6. 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.
    7. Chinedu Izuchukwu & Yekini Shehu & Chibueze C. Okeke, 2023. "Extension of forward-reflected-backward method to non-convex mixed variational inequalities," Journal of Global Optimization, Springer, vol. 86(1), pages 123-140, May.
    8. Jun-zuo Li & Yi-bin Xiao, 2025. "A Modified Popov Algorithm for Non-Monotone and Non-Lipschitzian Stochastic Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 205(3), pages 1-26, June.
    9. 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.
    10. S.-M. Grad & L. D. Muu & T. V. Thang, 2025. "Proximal-Type Algorithms for Solving Nonconvex Mixed Multivalued Quasi-Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 206(2), pages 1-26, August.
    11. 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.
    12. 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.
    13. Annamaria Barbagallo & Serena Guarino Lo Bianco, 2023. "A random time-dependent noncooperative equilibrium problem," Computational Optimization and Applications, Springer, vol. 84(1), pages 27-52, January.
    14. Huifu Xu & Dali Zhang, 2013. "Stochastic Nash equilibrium problems: sample average approximation and applications," Computational Optimization and Applications, Springer, vol. 55(3), pages 597-645, July.
    15. Shisheng Cui & Uday Shanbhag & Mathias Staudigl & Phan Vuong, 2022. "Stochastic relaxed inertial forward-backward-forward splitting for monotone inclusions in Hilbert spaces," Computational Optimization and Applications, Springer, vol. 83(2), pages 465-524, November.
    16. Shu Lu & Amarjit Budhiraja, 2013. "Confidence Regions for Stochastic Variational Inequalities," Mathematics of Operations Research, INFORMS, vol. 38(3), pages 545-568, August.
    17. Tong-tong Shang & Guo-ji Tang, 2023. "Mixed polynomial variational inequalities," Journal of Global Optimization, Springer, vol. 86(4), pages 953-988, August.
    18. Deng, Huaijun & Liu, Linna & Fang, Jianyin & Qu, Boyang & Huang, Quanzhen, 2023. "A novel improved whale optimization algorithm for optimization problems with multi-strategy and hybrid algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 794-817.
    19. Francesca Faraci & Baasansuren Jadamba & Fabio Raciti, 2016. "On Stochastic Variational Inequalities with Mean Value Constraints," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 675-693, November.
    20. Pang, Li-Ping & Chen, Shuang & Wang, Jin-He, 2015. "Risk management in portfolio applications of non-convex stochastic programming," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 565-575.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jglopt:v:91:y:2025:i:4:d:10.1007_s10898-024-01445-6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.