IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i8p1350-d796493.html
   My bibliography  Save this article

A New Alternative Regularization Method for Solving Generalized Equilibrium Problems

Author

Listed:
  • Yanlai Song

    (College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China
    These authors contributed equally to this work.)

  • Omar Bazighifan

    (Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
    Department of Mathematics, Faculty of Science, Hadhramout University, Mukalla 50512, Yemen
    These authors contributed equally to this work.)

Abstract

The purpose of this paper is to present a numerical method for solving a generalized equilibrium problem involving a Lipschitz continuous and monotone mapping in a Hilbert space. The proposed method can be viewed as an improvement of the Tseng’s extragradient method and the regularization method. We show that the iterative process constructed by the proposed method converges strongly to the smallest norm solution of the generalized equilibrium problem. Several numerical experiments are also given to illustrate the performance of the proposed method. One of the advantages of the proposed method is that it requires no knowledge of Lipschitz-type constants.

Suggested Citation

  • Yanlai Song & Omar Bazighifan, 2022. "A New Alternative Regularization Method for Solving Generalized Equilibrium Problems," Mathematics, MDPI, vol. 10(8), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1350-:d:796493
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/8/1350/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/8/1350/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gang Cai & Qiao-Li Dong & Yu Peng, 2021. "Strong Convergence Theorems for Solving Variational Inequality Problems with Pseudo-monotone and Non-Lipschitz Operators," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 447-472, February.
    2. 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.
    3. Yao, Yonghong & Cho, Yeol Je & Liou, Yeong-Cheng, 2011. "Algorithms of common solutions for variational inclusions, mixed equilibrium problems and fixed point problems," European Journal of Operational Research, Elsevier, vol. 212(2), pages 242-250, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yanlai Song & Omar Bazighifan, 2022. "Two Regularization Methods for the Variational Inequality Problem over the Set of Solutions of the Generalized Mixed Equilibrium Problem," Mathematics, MDPI, vol. 10(16), pages 1-20, August.

    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. Yanlai Song & Omar Bazighifan, 2022. "Modified Inertial Subgradient Extragradient Method with Regularization for Variational Inequality and Null Point Problems," Mathematics, MDPI, vol. 10(14), pages 1-17, July.
    2. Yanlai Song, 2021. "Hybrid Inertial Accelerated Algorithms for Solving Split Equilibrium and Fixed Point Problems," Mathematics, MDPI, vol. 9(21), pages 1-19, October.
    3. Shin-ya Matsushita & Li Xu, 2014. "On Finite Convergence of Iterative Methods for Variational Inequalities in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 701-715, June.
    4. Jamilu Abubakar & Poom Kumam & Habib ur Rehman & Abdulkarim Hassan Ibrahim, 2020. "Inertial Iterative Schemes with Variable Step Sizes for Variational Inequality Problem Involving Pseudomonotone Operator," Mathematics, MDPI, vol. 8(4), pages 1-25, April.
    5. Dang Hieu, 2017. "New subgradient extragradient methods for common solutions to equilibrium problems," Computational Optimization and Applications, Springer, vol. 67(3), pages 571-594, July.
    6. Yonghong Yao & Yeong-Cheng Liou & Ngai-Ching Wong, 2013. "Superimposed optimization methods for the mixed equilibrium problem and variational inclusion," Journal of Global Optimization, Springer, vol. 57(3), pages 935-950, November.
    7. Chinedu Izuchukwu & Yekini Shehu, 2021. "New Inertial Projection Methods for Solving Multivalued Variational Inequality Problems Beyond Monotonicity," Networks and Spatial Economics, Springer, vol. 21(2), pages 291-323, June.
    8. Timilehin O. Alakoya & Oluwatosin T. Mewomo & Yekini Shehu, 2022. "Strong convergence results for quasimonotone variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(2), pages 249-279, April.
    9. Yekini Shehu & Olaniyi S. Iyiola & Duong Viet Thong & Nguyen Thi Cam Van, 2021. "An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(2), pages 213-242, April.
    10. Dang Hieu & Pham Ky Anh & Le Dung Muu, 2019. "Modified extragradient-like algorithms with new stepsizes for variational inequalities," Computational Optimization and Applications, Springer, vol. 73(3), pages 913-932, July.
    11. Yanlai Song & Omar Bazighifan, 2022. "Regularization Method for the Variational Inequality Problem over the Set of Solutions to the Generalized Equilibrium Problem," Mathematics, MDPI, vol. 10(14), pages 1-20, July.
    12. Yanlai Song & Omar Bazighifan, 2022. "Two Regularization Methods for the Variational Inequality Problem over the Set of Solutions of the Generalized Mixed Equilibrium Problem," Mathematics, MDPI, vol. 10(16), pages 1-20, August.
    13. P. E. Maingé & M. L. Gobinddass, 2016. "Convergence of One-Step Projected Gradient Methods for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 146-168, October.
    14. Gang Cai & Aviv Gibali & Olaniyi S. Iyiola & Yekini Shehu, 2018. "A New Double-Projection Method for Solving Variational Inequalities in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 219-239, July.
    15. Boţ, R.I. & Csetnek, E.R. & Vuong, P.T., 2020. "The forward–backward–forward method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces," European Journal of Operational Research, Elsevier, vol. 287(1), pages 49-60.
    16. Seifu Endris Yimer & Poom Kumam & Anteneh Getachew Gebrie & Rabian Wangkeeree, 2019. "Inertial Method for Bilevel Variational Inequality Problems with Fixed Point and Minimizer Point Constraints," Mathematics, MDPI, vol. 7(9), pages 1-21, September.
    17. Xin He & Nan-jing Huang & Xue-song Li, 2022. "Modified Projection Methods for Solving Multi-valued Variational Inequality without Monotonicity," Networks and Spatial Economics, Springer, vol. 22(2), pages 361-377, June.
    18. Yiyin Cao & Yin Chen & Chuangyin Dang, 2024. "A Variant of the Logistic Quantal Response Equilibrium to Select a Perfect Equilibrium," Journal of Optimization Theory and Applications, Springer, vol. 201(3), pages 1026-1062, June.
    19. Lu-Chuan Ceng & Yekini Shehu & Jen-Chih Yao, 2022. "Modified Mann Subgradient-like Extragradient Rules for Variational Inequalities and Common Fixed Points Involving Asymptotically Nonexpansive Mappings," Mathematics, MDPI, vol. 10(5), pages 1-20, February.
    20. Yanlai Song & Mihai Postolache, 2021. "Modified Inertial Forward–Backward Algorithm in Banach Spaces and Its Application," Mathematics, MDPI, vol. 9(12), pages 1-17, June.

    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:gam:jmathe:v:10:y:2022:i:8:p:1350-:d:796493. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.