IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v148y2011i3d10.1007_s10957-010-9769-z.html
   My bibliography  Save this article

Iterative Algorithm for Solving Triple-Hierarchical Constrained Optimization Problem

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-010-9769-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-010-9769-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. "Triple Hierarchical Variational Inequalities, Systems of Variational Inequalities, and Fixed Point Problems," Mathematics, MDPI, vol. 7(2), pages 1-19, February.
    3. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Le Quang Thuy & Trinh Ngoc Hai, 2017. "A Projected Subgradient Algorithm for Bilevel Equilibrium Problems and Applications," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 411-431, November.
    2. F. U. Ogbuisi & F. O. Isiogugu & J. M. Ngnotchouye, 2021. "Approximating a common solution of extended split equality equilibrium and fixed point problems," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(1), pages 46-61, March.
    3. Lateef Olakunle Jolaoso & Adeolu Taiwo & Timilehin Opeyemi Alakoya & Oluwatosin Temitope Mewomo, 2020. "A Strong Convergence Theorem for Solving Pseudo-monotone Variational Inequalities Using Projection Methods," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 744-766, June.
    4. Phan Vuong & Jean Strodiot & Van Nguyen, 2014. "Projected viscosity subgradient methods for variational inequalities with equilibrium problem constraints in Hilbert spaces," Journal of Global Optimization, Springer, vol. 59(1), pages 173-190, May.
    5. Hideaki Iiduka, 2011. "Decentralized Algorithm for Centralized Variational Inequalities in Network Resource Allocation," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 525-540, December.
    6. Lu-Chuan Ceng & Qamrul Hasan Ansari & Jen-Chih Yao, 2011. "Iterative Methods for Triple Hierarchical Variational Inequalities in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 489-512, December.
    7. Phan Tu Vuong & Jean Jacques Strodiot & Van Hien Nguyen, 2012. "Extragradient Methods and Linesearch Algorithms for Solving Ky Fan Inequalities and Fixed Point Problems," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 605-627, November.
    8. Ying Liu & Hang Kong, 2019. "Strong convergence theorems for relatively nonexpansive mappings and Lipschitz-continuous monotone mappings in Banach spaces," Indian Journal of Pure and Applied Mathematics, Springer, vol. 50(4), pages 1049-1065, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:148:y:2011:i:3:d:10.1007_s10957-010-9769-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.