IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v85y2023i4d10.1007_s10898-022-01241-0.html
   My bibliography  Save this article

Weak and strong convergence of generalized proximal point algorithms with relaxed parameters

Author

Listed:
  • Hui Ouyang

    (University of British Columbia)

Abstract

In this work, we propose and study a framework of generalized proximal point algorithms associated with a maximally monotone operator. We indicate sufficient conditions on the regularization and relaxation parameters of generalized proximal point algorithms for the equivalence of the boundedness of the sequence of iterations generated by this algorithm and the non-emptiness of the zero set of the maximally monotone operator, and for the weak and strong convergence of the algorithm. Our results cover or improve many results on generalized proximal point algorithms in our references. Improvements of our results are illustrated by comparing our results with related known ones.

Suggested Citation

  • Hui Ouyang, 2023. "Weak and strong convergence of generalized proximal point algorithms with relaxed parameters," Journal of Global Optimization, Springer, vol. 85(4), pages 969-1002, April.
    • Handle: RePEc:spr:jglopt:v:85:y:2023:i:4:d:10.1007_s10898-022-01241-0
    DOI: 10.1007/s10898-022-01241-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-022-01241-0
    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/s10898-022-01241-0?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. Fenghui Wang, 2011. "A note on the regularized proximal point algorithm," Journal of Global Optimization, Springer, vol. 50(3), pages 531-535, July.
    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. Behzad Djafari Rouhani & Sirous Moradi, 2019. "Strong Convergence of Regularized New Proximal Point Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 864-882, June.
    2. Fenghui Wang & Huanhuan Cui, 2012. "On the contraction-proximal point algorithms with multi-parameters," Journal of Global Optimization, Springer, vol. 54(3), pages 485-491, November.
    3. Yamin Wang & Fenghui Wang & Hong-Kun Xu, 2016. "Error Sensitivity for Strongly Convergent Modifications of the Proximal Point Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 901-916, March.

    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:jglopt:v:85:y:2023:i:4:d:10.1007_s10898-022-01241-0. 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.