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Hybrid Extragradient-Like Viscosity Methods for Generalized Mixed Equilibrium Problems, Variational Inclusions, and Optimization Problems

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  • Lu-Chuan Ceng
  • Chi-Ming Chen
  • Chin-Tzong Pang

Abstract

We introduce and analyze a new hybrid extragradient-like viscosity iterative algorithm for finding a common solution of a generalized mixed equilibrium problem, a finite family of variational inclusions for maximal monotone and inverse strongly monotone mappings, and a fixed point problem of infinitely many nonexpansive mappings in a real Hilbert space. 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 which also solves an optimization problem.

Suggested Citation

  • Lu-Chuan Ceng & Chi-Ming Chen & Chin-Tzong Pang, 2014. "Hybrid Extragradient-Like Viscosity Methods for Generalized Mixed Equilibrium Problems, Variational Inclusions, and Optimization Problems," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-22, February.
    • Handle: RePEc:hin:jnlaaa:120172
    DOI: 10.1155/2014/120172
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