IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v41y1993i6p1164-1171.html
   My bibliography  Save this article

On the Convergence of a Hyperboloid Approximation Procedure for the Perturbed Euclidean Multifacility Location Problem

Author

Listed:
  • J. B. Rosen

    (University of Minnesota, Minneapolis, Minnesota)

  • G. L. Xue

    (University of Vermont, Burlington, Vermont)

Abstract

For the Euclidean single facility location problem, E. Weiszfeld proposed a simple closed-form iterative algorithm in 1937. Later, numerous authors proved that it is a convergent descent algorithm. In 1973, J. Eyster, J. White and W. Wierwille extended Weiszfeld's idea and proposed a Hyperboloid Approximation Procedure (HAP) for solving the Euclidean multifacility location problem. They believed, based on considerable computational experience, that the HAP always converges. In 1977, Ostresh proved that the HAP is a descent algorithm under certain conditions. In 1981, Morris proved that a variant of the HAP always converges. However, no convergence proof for the original HAP has ever been given. In this paper, we prove that the HAP is a descent algorithm and that it always converges to the minimizer of the objective function from any initial point.

Suggested Citation

  • J. B. Rosen & G. L. Xue, 1993. "On the Convergence of a Hyperboloid Approximation Procedure for the Perturbed Euclidean Multifacility Location Problem," Operations Research, INFORMS, vol. 41(6), pages 1164-1171, December.
    • Handle: RePEc:inm:oropre:v:41:y:1993:i:6:p:1164-1171
    DOI: 10.1287/opre.41.6.1164
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.41.6.1164
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.41.6.1164?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
    ---><---

    Citations

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


    Cited by:

    1. Jianlin Jiang & Liyun Ling & Yan Gu & Su Zhang & Yibing Lv, 2023. "Customized Alternating Direction Methods of Multipliers for Generalized Multi-facility Weber Problem," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 362-389, January.

    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:inm:oropre:v:41:y:1993:i:6:p:1164-1171. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.