Hybrid extragradient-like methods for generalized mixed equilibrium problems, systems of generalized equilibrium problems and optimization problems

Authors:
Lu-Chuan Ceng;Qamrul Hasan Ansari;Siegfried Schaible
Affiliations:
Department of Mathematics, Shanghai Normal University, Shanghai, China 200234 and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai, China;Department of Mathematics, Aligarh Muslim University, Aligarh, India 202 002;Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, Taiwan 32023
Venue:
Journal of Global Optimization
Year:
2012

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Abstract

In this paper, we introduce and analyze a new hybrid extragradient-like iterative algorithm for finding a common solution of a generalized mixed equilibrium problem, a system of generalized equilibrium problems and a fixed point problem of infinitely many non expansive mappings. Under some mild conditions, we prove the strong convergence of the sequence generated by the proposed algorithm to a common solution of these three problems. Such solution also solves an optimization problem. Several special cases are also discussed. The results presented in this paper are the supplement, extension, improvement and generalization of the previously known results in this area.