IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v21y1973i1p156-161.html
   My bibliography  Save this article

Further Reduction of Zero-One Polynomial Programming Problems to Zero-One linear Programming Problems

Author

Listed:
  • Fred Glover

    (University of Colorado, Boulder, Colorado)

  • Eugene Woolsey

    (Colorado School of Mines, Golden, Colorado)

Abstract

This paper gives rules that enable the transformation of a 0-1 polynomial programming problem into a 0-1 linear programming problem to be effected with reduced numbers of constraints. Rules are also given that provide reduced numbers of variables when the true variables of interest are not individual cross-product terms, but sums of such terms or polynomials of the form (∑ x j ) p .

Suggested Citation

  • Fred Glover & Eugene Woolsey, 1973. "Further Reduction of Zero-One Polynomial Programming Problems to Zero-One linear Programming Problems," Operations Research, INFORMS, vol. 21(1), pages 156-161, February.
    • Handle: RePEc:inm:oropre:v:21:y:1973:i:1:p:156-161
    DOI: 10.1287/opre.21.1.156
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.21.1.156
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.21.1.156?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. Buchheim, Christoph & Crama, Yves & Rodríguez-Heck, Elisabeth, 2019. "Berge-acyclic multilinear 0–1 optimization problems," European Journal of Operational Research, Elsevier, vol. 273(1), pages 102-107.
    2. Warren Adams & Hanif Sherali, 2005. "A Hierarchy of Relaxations Leading to the Convex Hull Representation for General Discrete Optimization Problems," Annals of Operations Research, Springer, vol. 140(1), pages 21-47, November.
    3. Alexander Mitsos, 2010. "Global solution of nonlinear mixed-integer bilevel programs," Journal of Global Optimization, Springer, vol. 47(4), pages 557-582, August.
    4. Teles, João P. & Castro, Pedro M. & Matos, Henrique A., 2013. "Univariate parameterization for global optimization of mixed-integer polynomial problems," European Journal of Operational Research, Elsevier, vol. 229(3), pages 613-625.
    5. Karthik Natarajan & Dongjian Shi & Kim-Chuan Toh, 2014. "A Probabilistic Model for Minmax Regret in Combinatorial Optimization," Operations Research, INFORMS, vol. 62(1), pages 160-181, February.
    6. Sven Mallach, 2018. "Compact linearization for binary quadratic problems subject to assignment constraints," 4OR, Springer, vol. 16(3), pages 295-309, September.
    7. Sven Mallach, 2021. "Inductive linearization for binary quadratic programs with linear constraints," 4OR, Springer, vol. 19(4), pages 549-570, December.
    8. D. Li & X. Sun & C. Liu, 2012. "An exact solution method for unconstrained quadratic 0–1 programming: a geometric approach," Journal of Global Optimization, Springer, vol. 52(4), pages 797-829, April.
    9. Fabio Furini & Emiliano Traversi, 2019. "Theoretical and computational study of several linearisation techniques for binary quadratic problems," Annals of Operations Research, Springer, vol. 279(1), pages 387-411, August.

    More about this item

    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:21:y:1973:i:1:p:156-161. 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.