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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    Lu-Chuan Ceng

  2. Scientific Computing Key Laboratory of Shanghai Universities, Shanghai, China

    Lu-Chuan Ceng

  3. Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, Uttar Pradesh, India

    Qamrul Hasan Ansari

  4. Department of Applied Mathematics, Chung Yuan Christian University, 32023, Chung-Li, Taiwan

    Siegfried Schaible

Authors
  1. Lu-Chuan Ceng
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  2. Qamrul Hasan Ansari
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  3. Siegfried Schaible
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Correspondence to Qamrul Hasan Ansari.

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Ceng, LC., Ansari, Q.H. & Schaible, S. Hybrid extragradient-like methods for generalized mixed equilibrium problems, systems of generalized equilibrium problems and optimization problems. J Glob Optim 53, 69–96 (2012). https://doi.org/10.1007/s10898-011-9703-4

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  • DOI: https://doi.org/10.1007/s10898-011-9703-4

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