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Iterative Algorithm for Solving Triple-Hierarchical Constrained Optimization Problem

Journal of Optimization Theory and Applications volume 148, pages 580–592 (2011)Cite this article

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.

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Authors and Affiliations

  1. Network Design Research Center, Kyushu Institute of Technology, Hibiya Kokusai Building 1F 107, 2-2-3 Uchisaiwai-cho, Chiyoda-ku, Tokyo, 100-0011, Japan

    Hideaki Iiduka

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  1. Hideaki Iiduka
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Correspondence to Hideaki Iiduka.

Additional information

Communicated by R. Glowinski.

I am sincerely grateful to Professor Angelo Miele of the Rice University for helping me improve the manuscript. This work was supported by the Japan Society for the Promotion of Science through a Grant-in-Aid (19001979).

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Iiduka, H. Iterative Algorithm for Solving Triple-Hierarchical Constrained Optimization Problem. J Optim Theory Appl 148, 580–592 (2011). https://doi.org/10.1007/s10957-010-9769-z

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  • DOI: https://doi.org/10.1007/s10957-010-9769-z

Keywords

  • Hierarchical constrained optimization problem
  • Variational inequality
  • Monotone operator
  • Nonexpansive mapping
  • Fixed point
  • Strong convergence