IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v186y2020i3d10.1007_s10957-020-01734-6.html
   My bibliography  Save this article

Demiclosedness Principles for Generalized Nonexpansive Mappings

Author

Listed:
  • Sedi Bartz

    (University of Massachusetts Lowell)

  • Rubén Campoy

    (University of Massachusetts Lowell)

  • Hung M. Phan

    (University of Massachusetts Lowell)

Abstract

Demiclosedness principles are powerful tools in the study of convergence of iterative methods. For instance, a multi-operator demiclosedness principle for firmly nonexpansive mappings is useful in obtaining simple and transparent arguments for the weak convergence of the shadow sequence generated by the Douglas–Rachford algorithm. We provide extensions of this principle, which are compatible with the framework of more general families of mappings such as cocoercive and conically averaged mappings. As an application, we derive the weak convergence of the shadow sequence generated by the adaptive Douglas–Rachford algorithm.

Suggested Citation

  • Sedi Bartz & Rubén Campoy & Hung M. Phan, 2020. "Demiclosedness Principles for Generalized Nonexpansive Mappings," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 759-778, September.
    • Handle: RePEc:spr:joptap:v:186:y:2020:i:3:d:10.1007_s10957-020-01734-6
    DOI: 10.1007/s10957-020-01734-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-020-01734-6
    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/s10957-020-01734-6?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.

    Citations

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


    Cited by:

    1. Sedi Bartz & Rubén Campoy & Hung M. Phan, 2022. "An Adaptive Alternating Direction Method of Multipliers," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 1019-1055, 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:186:y:2020:i:3:d:10.1007_s10957-020-01734-6. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.