IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v90y2025i3d10.1007_s10589-025-00652-5.html
   My bibliography  Save this article

On the use of restriction of the right-hand side in spatial branch-and-bound algorithms to ensure termination

Author

Listed:
  • Peter Kirst

    (Wageningen University & Research (WUR))

  • Christian Füllner

    (Karlsruhe Institute of Technology)

Abstract

Spatial branch-and-bound algorithms for global minimization of non-convex problems require both lower and upper bounding procedures that finally converge to a globally optimal value in order to ensure termination of these methods. Whereas convergence of lower bounds is commonly guaranteed for standard approaches in the literature, this does not always hold for upper bounds. For this reason, different so-called convergent upper bounding procedures are proposed. These methods are not always used in practice, possibly due to their additional complexity or possibly due to increasing runtimes on average problems. For that reason, in this article we propose a refinement of classical branch-and-bound methods that is simple to implement and comes with marginal overhead. We prove that this small improvement already leads to convergent upper bounds, and thus show that termination of spatial branch-and-bound methods is ensured under mild assumptions.

Suggested Citation

  • Peter Kirst & Christian Füllner, 2025. "On the use of restriction of the right-hand side in spatial branch-and-bound algorithms to ensure termination," Computational Optimization and Applications, Springer, vol. 90(3), pages 691-720, April.
    • Handle: RePEc:spr:coopap:v:90:y:2025:i:3:d:10.1007_s10589-025-00652-5
    DOI: 10.1007/s10589-025-00652-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-025-00652-5
    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/s10589-025-00652-5?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.

    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:90:y:2025:i:3:d:10.1007_s10589-025-00652-5. 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.