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Iterative methods for solving monotone equilibrium problems via dual gap functions

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Abstract

This paper proposes an iterative method for solving strongly monotone equilibrium problems by using gap functions combined with double projection-type mappings. Global convergence of the proposed algorithm is proved and its complexity is estimated. This algorithm is then coupled with the proximal point method to generate a new algorithm for solving monotone equilibrium problems. A class of linear equilibrium problems is investigated and numerical examples are implemented to verify our algorithms.

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Author notes

  1. Tran Dinh Quoc

    Present address: Department of Electrical Engineering (ESAT/SCD) and OPTEC, K.U. Leuven, Leuven, Belgium

Authors and Affiliations

  1. Hanoi University of Science, Hanoi, Vietnam

    Tran Dinh Quoc

  2. Institute of Mathematics, Hanoi, Vietnam

    Le Dung Muu

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  1. Tran Dinh Quoc
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  2. Le Dung Muu
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Correspondence to Tran Dinh Quoc.

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This paper is supported in part by NAFOSTED, Vietnam.

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Quoc, T.D., Muu, L.D. Iterative methods for solving monotone equilibrium problems via dual gap functions. Comput Optim Appl 51, 709–728 (2012). https://doi.org/10.1007/s10589-010-9360-4

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  • DOI: https://doi.org/10.1007/s10589-010-9360-4

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