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Inertial Extragradient Algorithms for Solving Equilibrium Problems

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Abstract

We introduce two new algorithms based upon the extragradient and inertial methods for solving pseudomonotone equilibrium problems in real Hilbert spaces. Strong converge and weak convergence of the proposed algorithms are established under some mild assumptions. Numerical results show that the proposed algorithms are more efficient than some existing methods for equilibrium problems.

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Acknowledgments

The authors would like to thank the editor and referee for careful reading, and constructive suggestions that allowed to improve significantly the presentation of this paper.

Funding

The first author is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant no. 101.01-2017.08.

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Authors and Affiliations

  1. Department of Mathematics, University of Transport and Communications, 3 Cau Giay Street, Hanoi, Vietnam

    Nguyen The Vinh

  2. TIMAS, Thang Long University, Hanoi, Vietnam

    Le Dung Muu

  3. Institute of Mathematics, VAST, Hanoi, Vietnam

    Le Dung Muu

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  1. Nguyen The Vinh
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  2. Le Dung Muu
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Correspondence to Le Dung Muu.

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Dedicated to Professor Le Tuan Hoa on the occasion of his 60th birthday

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Vinh, N.T., Muu, L.D. Inertial Extragradient Algorithms for Solving Equilibrium Problems. Acta Math Vietnam 44, 639–663 (2019). https://doi.org/10.1007/s40306-019-00338-1

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  • DOI: https://doi.org/10.1007/s40306-019-00338-1

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