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An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems

Author

Listed:
  • Yekini Shehu

    (Zhejiang Normal University
    Institute of Science and Technology (IST))

  • Olaniyi S. Iyiola

    (California University of Pennsylvania)

  • Duong Viet Thong

    (Duy Tan University)

  • Nguyen Thi Cam Van

    (National Economics University)

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.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:93:y:2021:i:2:d:10.1007_s00186-020-00730-w
    DOI: 10.1007/s00186-020-00730-w
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    References listed on IDEAS

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    1. Dang Hieu, 2018. "An inertial-like proximal algorithm for equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(3), pages 399-415, December.
    2. Thi Thu Van Nguyen & Jean Jacques Strodiot & Van Hien Nguyen, 2014. "Hybrid Methods for Solving Simultaneously an Equilibrium Problem and Countably Many Fixed Point Problems in a Hilbert Space," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 809-831, March.
    3. 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.
    4. Sergey I. Lyashko & Vladimir V. Semenov, 2016. "A New Two-Step Proximal Algorithm of Solving the Problem of Equilibrium Programming," Springer Optimization and Its Applications, in: Boris Goldengorin (ed.), Optimization and Its Applications in Control and Data Sciences, pages 315-325, Springer.
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