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Relaxed Inertial Subgradient Extragradient Algorithm for Solving Equilibrium Problems

Author

Listed:
  • Chidi Elijah Nwakpa

    (University of the Witwatersrand)

  • Austine Efut Ofem

    (University of KwaZulu-Natal)

  • Chinedu Izuchukwu

    (University of the Witwatersrand)

  • Chibueze Christian Okeke

    (University of the Witwatersrand)

Abstract

We propose a relaxed inertial subgradient extragradient algorithm for solving equilibrium problems in a real Hilbert space. Under the assumption that the associated bivariate function is pseudomonotone and satisfies the Lipschitzness, we establish that the generated sequence of our proposed algorithm converges weakly to the equilibria set of the equilibrium problem. Furthermore, we obtain a linear convergence rate under the assumption that the bifunction is strongly pseudomonotone. We apply our proposed algorithm to variational inequality and fixed point problems. Finally, we compare our method with other schemes in the literature and the improvement brought by our proposed method is evident in the numerical experiments considered in this paper.

Suggested Citation

  • Chidi Elijah Nwakpa & Austine Efut Ofem & Chinedu Izuchukwu & Chibueze Christian Okeke, 2025. "Relaxed Inertial Subgradient Extragradient Algorithm for Solving Equilibrium Problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 101(2), pages 331-371, April.
    • Handle: RePEc:spr:mathme:v:101:y:2025:i:2:d:10.1007_s00186-025-00894-3
    DOI: 10.1007/s00186-025-00894-3
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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. Cholamjiak, Watcharaporn & Suparatulatorn, Raweerote, 2023. "Strong convergence of a modified extragradient algorithm to solve pseudomonotone equilibrium and application to classification of diabetes mellitus," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    3. 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.
    4. Yonghong Yao & Abubakar Adamu & Yekini Shehu & Jen-Chih Yao, 2024. "Simple proximal-type algorithms for equilibrium problems," Journal of Global Optimization, Springer, vol. 89(4), pages 1069-1098, August.
    5. Pham Ky Anh & Trinh Ngoc Hai, 2019. "Novel self-adaptive algorithms for non-Lipschitz equilibrium problems with applications," Journal of Global Optimization, Springer, vol. 73(3), pages 637-657, March.
    6. Jun Yang & Hongwei Liu, 2020. "A self-adaptive method for pseudomonotone equilibrium problems and variational inequalities," Computational Optimization and Applications, Springer, vol. 75(2), pages 423-440, March.
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