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Steepest-Descent Approach to Triple Hierarchical Constrained Optimization Problems

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

Abstract

We introduce and analyze a hybrid steepest-descent algorithm by combining Korpelevich’s extragradient method, the steepest-descent method, and the averaged mapping approach to the gradient-projection algorithm. It is proven that under appropriate assumptions, the proposed algorithm converges strongly to the unique solution of a triple hierarchical constrained optimization problem (THCOP) over the common fixed point set of finitely many nonexpansive mappings, with constraints of finitely many generalized mixed equilibrium problems (GMEPs), finitely many variational inclusions, and a convex minimization problem (CMP) in a real Hilbert space.

Suggested Citation

  • Lu-Chuan Ceng & Cheng-Wen Liao & Chin-Tzong Pang & Ching-Feng Wen, 2014. "Steepest-Descent Approach to Triple Hierarchical Constrained Optimization Problems," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-19, August.
    • Handle: RePEc:hin:jnlaaa:264965
    DOI: 10.1155/2014/264965
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