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A self-adaptive extragradient–CQ method for a class of bilevel split equilibrium problem with application to Nash Cournot oligopolistic electricity market models

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Abstract

Van Quy (Optimization 68(4):753–771, 2018) established an extragradient–CQ algorithm for solving a class of bilevel split equilibrium problem. The step-size in the algorithm requires computation of a certain matrix norm which is costly. Moreover, bilevel problems often possess huge number of constraints and possibly require a robust and adaptive step-size algorithm to withstand failure in instances of real-world problems with large data sizes. In this paper, we propose a self-adaptive step-size extragradient–CQ algorithm for solving the same problem without prior knowledge of operator norm and provide a numerical example to demonstrate the effectiveness of our method.

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Acknowledgements

The authors are grateful to the editor and anonymous referees for their valuable suggestions and constructive comments which have improved this paper. Yusuf I. Suleiman is grateful to King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand, for providing state of the art research facilities to carry out this research work during his bench work in KMUTT. The second author, Habib ur Rehman is grateful for the support of the Petchra Pra Jom Klao Ph.D. Research Scholarship Board, KMUTT. Furthermore, this project was supported by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT.

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Authors and Affiliations

  1. Department of Mathematics, Kano University of Science and Technology, Wudil, Nigeria

    Yusuf I. Suleiman

  2. Fixed Point Research Laboratory, Fixed Point Theory and Applications Research Group, Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Habib ur Rehman & Poom Kumam

  3. Departments of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan

    Poom Kumam

  4. Department of Mathematics, ORT Braude College, 2161002, Karmiel, Israel

    Aviv Gibali

  5. The Center for Mathematics and Scientific Computation, University of Haifa, Mt. Carmel, 3498838, Haifa, Israel

    Aviv Gibali

Authors
  1. Yusuf I. Suleiman
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  2. Habib ur Rehman
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  3. Aviv Gibali
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  4. Poom Kumam
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Corresponding author

Correspondence to Poom Kumam.

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Communicated by Gabriel Haeser.

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Suleiman, Y.I., ur Rehman, H., Gibali, A. et al. A self-adaptive extragradient–CQ method for a class of bilevel split equilibrium problem with application to Nash Cournot oligopolistic electricity market models. Comp. Appl. Math. 39, 293 (2020). https://doi.org/10.1007/s40314-020-01338-w

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  • DOI: https://doi.org/10.1007/s40314-020-01338-w

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