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Iterative Algorithm for Solving Triple-Hierarchical Constrained Optimization Problem

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  • Hideaki Iiduka

    (Kyushu Institute of Technology)

Abstract

Many practical problems such as signal processing and network resource allocation are formulated as the monotone variational inequality over the fixed point set of a nonexpansive mapping, and iterative algorithms to solve these problems have been proposed. This paper discusses a monotone variational inequality with variational inequality constraint over the fixed point set of a nonexpansive mapping, which is called the triple-hierarchical constrained optimization problem, and presents an iterative algorithm for solving it. Strong convergence of the algorithm to the unique solution of the problem is guaranteed under certain assumptions.

Suggested Citation

  • Hideaki Iiduka, 2011. "Iterative Algorithm for Solving Triple-Hierarchical Constrained Optimization Problem," Journal of Optimization Theory and Applications, Springer, vol. 148(3), pages 580-592, March.
    • Handle: RePEc:spr:joptap:v:148:y:2011:i:3:d:10.1007_s10957-010-9769-z
    DOI: 10.1007/s10957-010-9769-z
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    References listed on IDEAS

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    1. H. Iiduka, 2009. "Hybrid Conjugate Gradient Method for a Convex Optimization Problem over the Fixed-Point Set of a Nonexpansive Mapping," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 463-475, March.
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    Cited by:

    1. Lu-Chuan Ceng & Xiaoye Yang, 2019. "Some Mann-Type Implicit Iteration Methods for Triple Hierarchical Variational Inequalities, Systems Variational Inequalities and Fixed Point Problems," Mathematics, MDPI, vol. 7(3), pages 1-20, February.
    2. Lu-Chuan Ceng & Qing Yuan, 2019. "Strong Convergence of a New Iterative Algorithm for Split Monotone Variational Inclusion Problems," Mathematics, MDPI, vol. 7(2), pages 1-12, January.
    3. Lu-Chuan Ceng & Qing Yuan, 2019. "Triple Hierarchical Variational Inequalities, Systems of Variational Inequalities, and Fixed Point Problems," Mathematics, MDPI, vol. 7(2), pages 1-19, February.
    4. Lu-Chuan Ceng & Qing Yuan, 2019. "Hybrid Mann Viscosity Implicit Iteration Methods for Triple Hierarchical Variational Inequalities, Systems of Variational Inequalities and Fixed Point Problems," Mathematics, MDPI, vol. 7(2), pages 1-24, February.

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