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HYBRID PROXIMAL POINT AND EXTRAGRADIENT ALGORITHMS FOR SOLVING EQUILIBRIUM PROBLEMS

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Abstract

We propose new iteration methods for finding a common point of the solution set of a pseudomonotone equilibrium problem and the solution set of a monotone equilibrium problem. The methods are based on both the extragradient-type method and the viscosity approximation method. We obtain weak convergence theorems for the sequences generated by these methods in a real Hilbert space.

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Acknowledgements

We are very grateful to the anonymous referee for his/her really helpful and constructive comments in improving the paper. This work is supported by the Vietnam Institute for Advanced Study in Mathematics (VIASM).

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Authors and Affiliations

  1. Department of Scientific Fundamentals, Posts and Telecommunications Institute of Technology, Hanoi, Vietnam

    Pham N. Anh

  2. Department of Natural Sciences, Duy Tan University, Danang, Vietnam

    Nguyen D. Hien

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  1. Pham N. Anh
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  2. Nguyen D. Hien
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Correspondence to Pham N. Anh.

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Anh, P.N., Hien, N.D. HYBRID PROXIMAL POINT AND EXTRAGRADIENT ALGORITHMS FOR SOLVING EQUILIBRIUM PROBLEMS. Acta Math Vietnam 39, 405–423 (2014). https://doi.org/10.1007/s40306-014-0070-3

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  • DOI: https://doi.org/10.1007/s40306-014-0070-3

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