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Iterative Schemes for Convex Minimization Problems with Constraints

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  • Lu-Chuan Ceng
  • Cheng-Wen Liao
  • Chin-Tzong Pang
  • Ching-Feng Wen

Abstract

We first introduce and analyze one implicit iterative algorithm for finding a solution of the minimization problem for a convex and continuously Fréchet differentiable functional, with constraints of several problems: the generalized mixed equilibrium problem, the system of generalized equilibrium problems, and finitely many variational inclusions in a real Hilbert space. We prove strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another implicit iterative algorithm for finding a fixed point of infinitely many nonexpansive mappings with the same constraints, and derive its strong convergence under mild assumptions.

Suggested Citation

  • Lu-Chuan Ceng & Cheng-Wen Liao & Chin-Tzong Pang & Ching-Feng Wen, 2014. "Iterative Schemes for Convex Minimization Problems with Constraints," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-22, May.
    • Handle: RePEc:hin:jnlaaa:209372
    DOI: 10.1155/2014/209372
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