IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v56y2008i2p512-518.html
   My bibliography  Save this article

Visualizing and Constructing Cycles in the Simplex Method

Author

Listed:
  • David Avis

    (School of Computer Science, McGill University, Montreal, Quebec, Canada H3A 2A6)

  • Bohdan Kaluzny

    (School of Computer Science, McGill University, Montreal, Quebec, Canada H3A 2A6)

  • David Titley-Péloquin

    (School of Computer Science, McGill University, Montreal, Quebec, Canada H3A 2A6)

Abstract

Most examples of cycling in the simplex method are given without explanation of how they were constructed. An exception is Beale's example built around the geometry of the dual simplex method in the plane [Beale, E. 1955. Cycling in the dual simplex method. Naval Res. Logist. Quart. 2 (4) 269--275]. Using this approach, we give a simple geometric explanation for a number of examples of cycling in the simplex method, including Hoffman's original example [Hoffman, A. 1953. Cycling in the Simplex Algorithm . National Bureau of Standards, Washington, D.C.]. This gives rise to a simple method for generating examples with cycles.

Suggested Citation

  • David Avis & Bohdan Kaluzny & David Titley-Péloquin, 2008. "Visualizing and Constructing Cycles in the Simplex Method," Operations Research, INFORMS, vol. 56(2), pages 512-518, April.
    • Handle: RePEc:inm:oropre:v:56:y:2008:i:2:p:512-518
    DOI: 10.1287/opre.1070.0474
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1070.0474
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1070.0474?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
    ---><---

    References listed on IDEAS

    as
    1. Zhang, Shuzhong, 1999. "New variants of finite criss-cross pivot algorithms for linear programming," European Journal of Operational Research, Elsevier, vol. 116(3), pages 607-614, August.
    Full references (including those not matched with items on IDEAS)

    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. Illes, Tibor & Terlaky, Tamas, 2002. "Pivot versus interior point methods: Pros and cons," European Journal of Operational Research, Elsevier, vol. 140(2), pages 170-190, July.
    2. Akkeles, Arif A. & Balogh, Laszlo & Illes, Tibor, 2004. "New variants of the criss-cross method for linearly constrained convex quadratic programming," European Journal of Operational Research, Elsevier, vol. 157(1), pages 74-86, August.
    3. Konstantinos Paparrizos & Nikolaos Samaras & Angelo Sifaleras, 2015. "Exterior point simplex-type algorithms for linear and network optimization problems," Annals of Operations Research, Springer, vol. 229(1), pages 607-633, June.

    More about this item

    Keywords

    linear programming theory;

    Statistics

    Access and download statistics

    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:56:y:2008:i:2:p:512-518. 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: 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.