IDEAS home Printed from https://ideas.repec.org/h/spr/oprchp/978-3-030-48439-2_14.html
   My bibliography  Save this book chapter

A Steepest Feasible Direction Extension of the Simplex Method

In: Operations Research Proceedings 2019

Author

Listed:
  • Biressaw C. Wolde

    (Linköping University)

  • Torbjörn Larsson

    (Linköping University)

Abstract

We present a feasible direction approach to general linear programming, which can be embedded in the simplex method although it works with non-edge feasible directions. The feasible direction used is the steepest in the space of all variables, or an approximation thereof. Given a basic feasible solution, the problem of finding a (near-)steepest feasible direction is stated as a strictly convex quadratic program in the space of the non-basic variables and with only non-negativity restrictions. The direction found is converted into an auxiliary non-basic column, known as an external column. Our feasible direction approach allows several computational strategies. First, one may choose how frequently external columns are created. Secondly, one may choose how accurately the direction-finding quadratic problem is solved. Thirdly, near-steepest directions can be obtained from low-dimensional restrictions of the direction-finding quadratic program or by the use of approximate algorithms for this program.

Suggested Citation

  • Biressaw C. Wolde & Torbjörn Larsson, 2020. "A Steepest Feasible Direction Extension of the Simplex Method," Operations Research Proceedings, in: Janis S. Neufeld & Udo Buscher & Rainer Lasch & Dominik Möst & Jörn Schönberger (ed.), Operations Research Proceedings 2019, pages 113-121, Springer.
    • Handle: RePEc:spr:oprchp:978-3-030-48439-2_14
    DOI: 10.1007/978-3-030-48439-2_14
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    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:oprchp:978-3-030-48439-2_14. 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.