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An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems

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Abstract

The paper introduces an inertial extragradient subgradient method with self-adaptive step sizes for solving equilibrium problems in real Hilbert spaces. Weak convergence of the proposed method is obtained under the condition that the bifunction is pseudomonotone and Lipchitz continuous. Linear convergence is also given when the bifunction is strongly pseudomonotone and Lipchitz continuous. Numerical implementations and comparisons with other related inertial methods are given using test problems including a real-world application to Nash–Cournot oligopolistic electricity market equilibrium model.

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Acknowledgements

The authors are grateful to the two referees and the Associate Editor for their comments and suggestions which have improved the earlier version of the paper greatly. The project of Yekini Shehu has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Program (FP7 - 2007-2013) (Grant agreement No. 616160).

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, People’s Republic of China

    Yekini Shehu

  2. Institute of Science and Technology (IST), Am Campus 1, 3400, Klosterneuburg, Vienna, Austria

    Yekini Shehu

  3. Department of Mathematics and Physical Sciences, California University of Pennsylvania, California, PA, USA

    Olaniyi S. Iyiola

  4. Institute of Research and Development, Duy Tan University, Da Nang, 550000, Vietnam

    Duong Viet Thong

  5. Faculty of Economics Mathematics, National Economics University, Hanoi City, Vietnam

    Nguyen Thi Cam Van

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  1. Yekini Shehu
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  2. Olaniyi S. Iyiola
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  3. Duong Viet Thong
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  4. Nguyen Thi Cam Van
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Correspondence to Duong Viet Thong.

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Shehu, Y., Iyiola, O.S., Thong, D.V. et al. An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems. Math Meth Oper Res 93, 213–242 (2021). https://doi.org/10.1007/s00186-020-00730-w

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  • DOI: https://doi.org/10.1007/s00186-020-00730-w

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