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Iterative Algorithm for Solving Triple-Hierarchical Constrained Optimization Problem

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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

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