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Convergence analysis of a new algorithm for strongly pseudomontone equilibrium problems

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Abstract

The paper introduces and analyzes the convergence of a new iterative algorithm for approximating solutions of equilibrium problems involving strongly pseudomonotone and Lipschitz-type bifunctions in Hilbert spaces. The algorithm uses a stepsize sequence which is non-increasing, diminishing, and non-summable. This leads to the main advantage of the algorithm, namely that the construction of solution approximations and the proof of its convergence are done without the prior knowledge of the modulus of strong pseudomonotonicity and Lipschitz-type constants of bifunctions. The strongly convergent theorem is established under suitable assumptions. The paper also discusses the assumptions used in the formulation of the convergent theorem. Several numerical results are reported to illustrate the behavior of the algorithm with different sequences of stepsizes and also to compare it with others.

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Acknowledgements

The author would like to thank the Associate Editor and two anonymous referees for their valuable comments and suggestions which helped us very much in improving the original version of this paper. The guidance of Profs. P. K. Anh and L. D. Muu is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mathematics, Vietnam National University, Hanoi, Vietnam

    Dang Van Hieu

  2. Department of Mathematics, College of Air Force, Nhatrang, Vietnam

    Dang Van Hieu

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  1. Dang Van Hieu
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Correspondence to Dang Van Hieu.

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Van Hieu, D. Convergence analysis of a new algorithm for strongly pseudomontone equilibrium problems. Numer Algor 77, 983–1001 (2018). https://doi.org/10.1007/s11075-017-0350-9

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  • DOI: https://doi.org/10.1007/s11075-017-0350-9

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