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Gradient projection-type algorithms for solving equilibrium problems and its applications

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Abstract

In this paper, we study strongly pseudo-monotone equilibrium problems in real Hilbert and introduce two simple subgradient-type methods for solving it. The advantages of our schemes are the simplicity of their algorithmic structure which consists of only one projection onto the feasible set and there is no need to solve any strongly convex programming problem, which is often used in related methods in the literature. Under mild and standard assumptions, strong convergence theorems of the proposed algorithms are established. We test and compare the performances of our schemes with some related methods in the literature for solving the Nash–Cournot oligopolistic equilibrium model.

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Acknowledgements

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

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Authors and Affiliations

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

    Nguyen The Vinh

  2. Department of Mathematics, ORT Braude College, 2161002, Karmiel, Israel

    Aviv Gibali

  3. The Center for Mathematics and Scientific Computation, University of Haifa, Mt. Carmel, 3498838, Haifa, Israel

    Aviv Gibali

Authors
  1. Nguyen The Vinh
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  2. Aviv Gibali
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Correspondence to Aviv Gibali.

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Communicated by Gabriel Haeser.

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Vinh, N.T., Gibali, A. Gradient projection-type algorithms for solving equilibrium problems and its applications. Comp. Appl. Math. 38, 119 (2019). https://doi.org/10.1007/s40314-019-0894-5

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