IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v180y2019i2d10.1007_s10957-018-1387-1.html
   My bibliography  Save this article

Optimization for the Sum of Finite Functions Over the Solution Set of Split Equality Optimization Problems with Applications

Author

Listed:
  • Lai-Jiu Lin

    (National Changhua University of Education)

Abstract

In this paper, we adopt an iterative approach to solve the class of optimization problem for the sum of finite functions over split equality optimization problems for the sum of two functions. This type of problem contains many optimization problems, and bilevel problems, as well as split equality problems, and split feasibility problems as special cases. Here, we are able to establish a strong convergence theorem for an iterative method for solving this problem. As consequences of this convergence theorem, we study the following problems: optimization for the sum of finite functions over the common solution set of optimization problems for the sum of two functions; optimization for the sum of finite functions; optimization for the sum of finite functions with split equality inconsistent feasibility constraints; optimization for the sum of finite functions over the solution set for split equality constrained quadratic signal recovery problem; optimization for the sum of finite functions over the solution set of generalized split equality multiple set feasibility problem, and optimization for the sum of finite functions over the solution set of split equality linear equations problem. We use simultaneous iteration to establish strong convergence theorems for these problems. Our results generalize and improve many existing theorems for these types of problems in the literature and will have applications in nonlinear analysis, optimization problems and signal processing problems.

Suggested Citation

  • Lai-Jiu Lin, 2019. "Optimization for the Sum of Finite Functions Over the Solution Set of Split Equality Optimization Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 180(2), pages 451-479, February.
  • Handle: RePEc:spr:joptap:v:180:y:2019:i:2:d:10.1007_s10957-018-1387-1
    DOI: 10.1007/s10957-018-1387-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-018-1387-1
    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/s10957-018-1387-1?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. Abdellatif Moudafi, 2013. "Alternating CQ-Algorithms For Convex Feasibility And Split Fixed-Point Problems," Documents de Travail 2013-02, CEREGMIA, Université des Antilles et de la Guyane.
    Full references (including those not matched with items on IDEAS)

    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. Shih-sen Chang & Lin Wang & Xiong Rui Wang & Gang Wang, 2015. "General Split Equality Equilibrium Problems with Application to Split Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 377-390, August.
    2. Dianlu Tian & Lining Jiang & Luoyi Shi, 2019. "Gradient Methods with Selection Technique for the Multiple-Sets Split Equality Problem," Mathematics, MDPI, vol. 7(10), pages 1-10, October.

    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:180:y:2019:i:2:d:10.1007_s10957-018-1387-1. 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.