IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v52y2012i3p825-843.html
   My bibliography  Save this article

An efficient simultaneous method for the constrained multiple-sets split feasibility problem

Author

Listed:
  • Wenxing Zhang
  • Deren Han
  • Xiaoming Yuan

Abstract

The multiple-sets split feasibility problem (MSFP) captures various applications arising in many areas. Recently, by introducing a function measuring the proximity to the involved sets, Censor et al. proposed to solve the MSFP via minimizing the proximity function, and they developed a class of simultaneous methods to solve the resulting constrained optimization model numerically. In this paper, by combining the ideas of the proximity function and the operator splitting methods, we propose an efficient simultaneous method for solving the constrained MSFP. The efficiency of the new method is illustrated by some numerical experiments. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Wenxing Zhang & Deren Han & Xiaoming Yuan, 2012. "An efficient simultaneous method for the constrained multiple-sets split feasibility problem," Computational Optimization and Applications, Springer, vol. 52(3), pages 825-843, July.
  • Handle: RePEc:spr:coopap:v:52:y:2012:i:3:p:825-843
    DOI: 10.1007/s10589-011-9429-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-011-9429-8
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s10589-011-9429-8?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. D. Han, 2007. "Inexact Operator Splitting Methods with Selfadaptive Strategy for Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 132(2), pages 227-243, February.
    2. Z. K. Jiang & X. M. Yuan, 2010. "New Parallel Descent-like Method for Solving a Class of Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 311-323, May.
    3. Bing-Sheng He, 2009. "Parallel splitting augmented Lagrangian methods for monotone structured variational inequalities," Computational Optimization and Applications, Springer, vol. 42(2), pages 195-212, 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. Hongjin He & Chen Ling & Hong-Kun Xu, 2015. "A Relaxed Projection Method for Split Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 213-233, July.
    2. X. Wang & S. Li & X. Kou & Q. Zhang, 2015. "A new alternating direction method for linearly constrained nonconvex optimization problems," Journal of Global Optimization, Springer, vol. 62(4), pages 695-709, August.
    3. Yuning Yang & Qingzhi Yang & Su Zhang, 2014. "Modified Alternating Direction Methods for the Modified Multiple-Sets Split Feasibility Problems," Journal of Optimization Theory and Applications, Springer, vol. 163(1), pages 130-147, October.

    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. Min Tao & Xiaoming Yuan, 2012. "An inexact parallel splitting augmented Lagrangian method for monotone variational inequalities with separable structures," Computational Optimization and Applications, Springer, vol. 52(2), pages 439-461, June.
    2. Hongjin He & Chen Ling & Hong-Kun Xu, 2015. "A Relaxed Projection Method for Split Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 213-233, July.
    3. Xiaomei Dong & Xingju Cai & Deren Han & Zhili Ge, 2020. "Solving a Class of Variational Inequality Problems with a New Inexact Strategy," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(01), pages 1-20, January.
    4. Kun Jin & Yevgeniy Vorobeychik & Mingyan Liu, 2021. "Multi-Scale Games: Representing and Solving Games on Networks with Group Structure," Papers 2101.08314, arXiv.org.
    5. Liusheng Hou & Hongjin He & Junfeng Yang, 2016. "A partially parallel splitting method for multiple-block separable convex programming with applications to robust PCA," Computational Optimization and Applications, Springer, vol. 63(1), pages 273-303, January.
    6. Min Zhang & Deren Han & Gang Qian & Xihong Yan, 2012. "A New Decomposition Method for Variational Inequalities with Linear Constraints," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 675-695, March.
    7. Z. K. Jiang & X. M. Yuan, 2010. "New Parallel Descent-like Method for Solving a Class of Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 311-323, May.
    8. Zhongming Chen & Li Wan & Qingzhi Yang, 2014. "An Inexact Alternating Direction Method for Structured Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 439-459, November.
    9. Deren Han & Wei Xu & Hai Yang, 2010. "Solving a class of variational inequalities with inexact oracle operators," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(3), pages 427-452, June.
    10. Deren Han & Xiaoming Yuan & Wenxing Zhang & Xingju Cai, 2013. "An ADM-based splitting method for separable convex programming," Computational Optimization and Applications, Springer, vol. 54(2), pages 343-369, March.
    11. Yaning Jiang & Deren Han & Xingju Cai, 2022. "An efficient partial parallel method with scaling step size strategy for three-block convex optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(3), pages 383-419, December.
    12. K. Wang & D. R. Han & L. L. Xu, 2013. "A Parallel Splitting Method for Separable Convex Programs," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 138-158, October.
    13. Pham Ngoc Anh & Qamrul Hasan Ansari & Ho Phi Tu, 2023. "DC auxiliary principle methods for solving lexicographic equilibrium problems," Journal of Global Optimization, Springer, vol. 85(1), pages 129-153, January.

    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:coopap:v:52:y:2012:i:3:p:825-843. 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.