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An inertial extragradient algorithm for equilibrium and generalized split null point problems

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Abstract

This paper provides iterative construction of a common solution associated with a class of equilibrium problems and split convex feasibility problems. In particular, we are interested in the equilibrium problems defined with respect to the pseudomonotone and Lipschitz-type continuous equilibrium problem together with the generalized split null point problems in real Hilbert spaces. We propose an iterative algorithm that combines the hybrid extragradient method with the inertial acceleration method. The analysis of the proposed algorithm comprises theoretical results concerning strong convergence under suitable set of constraints and numerical results concerning the viability of the proposed algorithm with respect to various real-world applications.

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Acknowledgements

The authors wish to thank the anonymous referees for their comments and suggestions. The authors (Y. Arfat, P. Kumam and P.S. Ngiamsunthorn) acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Moreover, this project is funded by National Council of Thailand (NRCT) under Research Grants for Talented Mid-Career Researchers (Contract no. N41A640089). The author Y. Arfat was supported by the Petchra Pra Jom Klao Ph.D Research Scholarship from King Mongkut’s University of Technology Thonburi, Thailand (Grant No.16/2562). The author (M. A. A. Khan) gratefully acknowledges the support provided by the Higher Education Commission of Pakistan through project No. NRPU 20-14574.

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Authors and Affiliations

  1. KMUTT Fixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Yasir Arfat & Poom Kumam

  2. Center of Excellence in Theoretical and Computational Science (TaCS-CoE), SCL 802 Fixed Point Laboratory, Science Laboratory Building, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Poom Kumam

  3. Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan

    Poom Kumam

  4. Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, 54000, Pakistan

    Muhammad Aqeel Ahmad Khan

  5. Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Parinya Sa Ngiamsunthorn

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  1. Yasir Arfat
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  2. Poom Kumam
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  3. Muhammad Aqeel Ahmad Khan
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  4. Parinya Sa Ngiamsunthorn
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Correspondence to Poom Kumam or Muhammad Aqeel Ahmad Khan.

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Communicated by: Thanh Tran

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All authors contributed equally and significantly in writing this article. All authors read and approved the final manuscript.

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This article belongs to the Topical Collection: Mathematics of Computation and Optimisation Guest Editors: Jerome Droniou, Andrew Eberhard, Guoyin Li, Russell Luke, Thanh Tran

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Arfat, Y., Kumam, P., Khan, M.A.A. et al. An inertial extragradient algorithm for equilibrium and generalized split null point problems. Adv Comput Math 48, 53 (2022). https://doi.org/10.1007/s10444-021-09920-4

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