Iterative methods for solving monotone equilibrium problems via dual gap functions

Authors:
Tran Dinh Quoc;Le Dung Muu
Affiliations:
Hanoi University of Science, Hanoi, Vietnam and Department of Electrical Engineering (ESAT/SCD) and OPTEC, K.U. Leuven, Leuven, Belgium;Institute of Mathematics, Hanoi, Vietnam
Venue:
Computational Optimization and Applications
Year:
2012

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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.