IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v58y2014i1p189-203.html
   My bibliography  Save this article

On the exhaustivity of simplicial partitioning

Author

Listed:
  • Peter Dickinson

Abstract

During the last 40 years, simplicial partitioning has been shown to be highly useful, including in the field of nonlinear optimization, specifically global optimization. In this article, we consider results on the exhaustivity of simplicial partitioning schemes. We consider conjectures on this exhaustivity which seem at first glance to be true (two of which have been stated as true in published articles). However, we will provide counter-examples to these conjectures. We also provide a new simplicial partitioning scheme, which provides a lot of freedom, whilst guaranteeing exhaustivity. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Peter Dickinson, 2014. "On the exhaustivity of simplicial partitioning," Journal of Global Optimization, Springer, vol. 58(1), pages 189-203, January.
    • Handle: RePEc:spr:jglopt:v:58:y:2014:i:1:p:189-203
    DOI: 10.1007/s10898-013-0040-7
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-013-0040-7
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-013-0040-7?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. Hendrix, Eligius M.T. & Casado, Leocadio G. & Garcí­a, Inmaculada, 2008. "The semi-continuous quadratic mixture design problem: Description and branch-and-bound approach," European Journal of Operational Research, Elsevier, vol. 191(3), pages 803-815, December.
    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. Mohammadreza Safi & Seyed Saeed Nabavi & Richard J. Caron, 2021. "A modified simplex partition algorithm to test copositivity," Journal of Global Optimization, Springer, vol. 81(3), pages 645-658, November.
    2. Peiping Shen & Dianxiao Wu & Kaimin Wang, 2023. "Globally minimizing a class of linear multiplicative forms via simplicial branch-and-bound," Journal of Global Optimization, Springer, vol. 86(2), pages 303-321, June.
    3. Akihiro Tanaka & Akiko Yoshise, 2018. "LP-based tractable subcones of the semidefinite plus nonnegative cone," Annals of Operations Research, Springer, vol. 265(1), pages 155-182, 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. Juan Herrera & Leocadio Casado & Eligius Hendrix & Inmaculada García, 2014. "Pareto optimality and robustness in bi-blending problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 254-273, April.
    2. L. Casado & I. García & B. Tóth & E. Hendrix, 2011. "On determining the cover of a simplex by spheres centered at its vertices," Journal of Global Optimization, Springer, vol. 50(4), pages 645-655, August.
    3. James M. Calvin & Antanas Žilinskas, 2014. "On a Global Optimization Algorithm for Bivariate Smooth Functions," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 528-547, November.

    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:58:y:2014:i:1:p:189-203. 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.