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Modified basic projection methods for a class of equilibrium problems

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Abstract

Projection methods are a popular class of methods for solving equilibrium problems. In this paper, we propose approximate one projection methods for solving a class of equilibrium problems, where the cost bifunctions are paramonotone, the feasible sets are defined by a continuous convex function inequality and not necessarily differentiable in the Euclidean space \(\mathcal R^{s}\). At each main iteration step in our algorithms, the usual projections onto the feasible set are replaced by computing inexact subgradients and one projection onto the intersection of two halfspaces containing the solution set of the equilibrium problems. Then, by choosing suitable parameters, we prove convergence of the whole generated sequence to a solution of the problems, under only the assumptions of continuity and paramonotonicity of the bifunctions. Finally, we present some computational examples to illustrate the assumptions of the proposed algorithms.

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Acknowledgments

We are very grateful to two anonymous referees for their really helpful and constructive comments that helped us very much in improving the paper.

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Authors and Affiliations

  1. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Pham Ngoc Anh

  2. Department of Mathematics, Haiphong University, Haiphong, Vietnam

    Tran T. H. Anh

  3. Office of Scientific Research and Technology, Duy Tan University, Da Nang, Vietnam

    Nguyen D. Hien

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  1. Pham Ngoc Anh
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  2. Tran T. H. Anh
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  3. Nguyen D. Hien
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Correspondence to Pham Ngoc Anh.

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Anh, P.N., Anh, T.T.H. & Hien, N.D. Modified basic projection methods for a class of equilibrium problems. Numer Algor 79, 139–152 (2018). https://doi.org/10.1007/s11075-017-0431-9

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