IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v107y2000i1d10.1023_a1004656716776.html
   My bibliography  Save this article

Finiteness Result for the Simplicial Branch-and-Bound Algorithm Based on ω-Subdivisions

Author

Listed:
  • M. Locatelli

    (Universitá di Torino)

  • U. Raber

    (University of Trier)

Abstract

The question of the finiteness of simplicial branch-and-bound algorithms employing only ω-subdivisions is considered. In Ref. 1, it was shown that this algorithm is convergent; here, it is proved that the algorithm is also finite if two assumptions are fulfilled. The first assumption requires the function values at vertices of the initial simplex to be lower than the optimal value of the problem. The second assumption requires each vertex of the initial simplex to violate at most one of the constraints defining the feasible polytope. The first assumption is mild from a theoretical point of view; the second assumption is strong, but holds always for instance when the feasible region is a hypercube.

Suggested Citation

  • M. Locatelli & U. Raber, 2000. "Finiteness Result for the Simplicial Branch-and-Bound Algorithm Based on ω-Subdivisions," Journal of Optimization Theory and Applications, Springer, vol. 107(1), pages 81-88, October.
    • Handle: RePEc:spr:joptap:v:107:y:2000:i:1:d:10.1023_a:1004656716776
    DOI: 10.1023/A:1004656716776
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1004656716776
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1004656716776?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. M. Locatelli & U. Raber, 2000. "On Convergence of the Simplicial Branch-and-Bound Algorithm Based on ω-Subdivisions," Journal of Optimization Theory and Applications, Springer, vol. 107(1), pages 69-79, October.
    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. Takahito Kuno & Tomohiro Ishihama, 2016. "A generalization of $$\omega $$ ω -subdivision ensuring convergence of the simplicial algorithm," Computational Optimization and Applications, Springer, vol. 64(2), pages 535-555, June.
    2. Takahito Kuno & Paul Buckland, 2012. "A convergent simplicial algorithm with ω-subdivision and ω-bisection strategies," Journal of Global Optimization, Springer, vol. 52(3), pages 371-390, March.
    3. Takahito Kuno, 2018. "A modified simplicial algorithm for convex maximization based on an extension of $$\omega $$ ω -subdivision," Journal of Global Optimization, Springer, vol. 71(2), pages 297-311, June.

    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. Takahito Kuno, 2018. "A modified simplicial algorithm for convex maximization based on an extension of $$\omega $$ ω -subdivision," Journal of Global Optimization, Springer, vol. 71(2), pages 297-311, June.

    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:107:y:2000:i:1:d:10.1023_a:1004656716776. 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.