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A new approach to the Korpelevich method for solving pseudomonotone equilibrium problems

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Abstract

The Korpelevich method is an algorithm which is used to find solutions to equilibrium problems. These problems are mathematical models which are used in economics, game theory, and engineering. Pseudomonotone equilibrium problems are a specific class of equilibrium problems that involve a weakened form of monotonicity. This work introduces a novel approach to applying the Korpelevich method to solving pseudomonotone equilibrium problems. We present a weak convergence theorem and linear convergence of the proposed method under some suitable conditions. Finally, a numerical example of a Nash-Cournot oligopolistic electricity market equilibrium model is given to complement the theoretical discussion and strengthen the evidence for the capabilities of our new approach.

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The data sets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

All the authors are grateful to two anonymous referees for their useful comments and helpful suggestions.

Funding

Simeon Reich was partially supported by the Israel Science Foundation (Grant 820/17), by the Fund for the Promotion of Research at the Technion (Grant 2001893), and by the Technion General Research Fund (Grant 2016723). Xiao-Huan Li was partially supported by the National Natural Science Foundation of China (12371305) and ShandongProvince Natural Science Foundation (ZR2023MA020). This research has been done under the research projectQG.23.04 of Vietnam National University, Hanoi.

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Authors and Affiliations

  1. Faculty of Mathematical Economics, National Economics University, Hanoi City, Vietnam

    Duong Viet Thong & Dang Huy Ngan

  2. School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255000, China

    Xiao-Huan Li

  3. Department of Mathematics, The Technion – Israel Institute of Technology, 32000, Haifa, Israel

    Simeon Reich

  4. Tianjin Key Laboratory for Advanced Signal Processing and College of Science, Civil Aviation University of China, Tianjin, 300300, China

    Qiao-Li Dong

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  1. Duong Viet Thong
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  2. Xiao-Huan Li
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  3. Simeon Reich
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  4. Qiao-Li Dong
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  5. Dang Huy Ngan
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Contributions

D. V. Thong, Simeon Reich, and Dang Huy Ngan wrote the main manuscript text, Xiao-Huan Li and Qiao-Li Dong prepared Tables 1 and 2 and Figs. 1 and 2. All authors reviewed the manuscript carefully. All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

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Correspondence to Duong Viet Thong.

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Dedicated to Professor Pham Ky Anh on the occasion of his 75th birthday.

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Thong, D.V., Li, XH., Reich, S. et al. A new approach to the Korpelevich method for solving pseudomonotone equilibrium problems. Numer Algor (2024). https://doi.org/10.1007/s11075-024-01813-z

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