IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v42y1996i12p1719-1731.html
   My bibliography  Save this article

Combining Interior-Point and Pivoting Algorithms for Linear Programming

Author

Listed:
  • Erling D. Andersen

    (Department of Management, Odense University, DK-5230 Odense M, Denmark)

  • Yinyu Ye

    (Department of Management Sciences, The University of Iowa, Iowa City, Iowa 52242)

Abstract

We propose a new approach to combine linear programming (LP) interior-point and simplex pivoting algorithms. In any iteration of an interior-point algorithm we construct a related LP problem, which approximates the original problem, with a known (strictly) complementary primal-dual solution pair. Thus, we can apply Megiddo's (Megiddo, N. 1991. On finding primal- and dual-optimal bases. ORSA J. Comput. 3(1) 63--65.) pivoting procedure to compute an optimal basis for the approximate problem in strongly polynomial time. We show that, if the approximate problem is constructed from an interior-point iterate sufficiently close to the optimal face, then any optimal basis of the approximate problem is an optimal basis for the original problem. If the LP data are rational, the total number of interior-point iterations to create such a sufficient approximate problem is bounded by a polynomial in the data size. We develop a modification of Megiddo's procedure and discuss several implementation issues in solving the approximate problem. We also report encouraging computational results for this combined approach.

Suggested Citation

  • Erling D. Andersen & Yinyu Ye, 1996. "Combining Interior-Point and Pivoting Algorithms for Linear Programming," Management Science, INFORMS, vol. 42(12), pages 1719-1731, December.
    • Handle: RePEc:inm:ormnsc:v:42:y:1996:i:12:p:1719-1731
    DOI: 10.1287/mnsc.42.12.1719
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.42.12.1719
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.42.12.1719?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. Erling D. Andersen, 1999. "On Exploiting Problem Structure in a Basis Identification Procedure for Linear Programming," INFORMS Journal on Computing, INFORMS, vol. 11(1), pages 95-103, February.
    2. Liu, Yanwu & Tu, Yan & Zhang, Zhongzhen, 2021. "The row pivoting method for linear programming," Omega, Elsevier, vol. 100(C).
    3. B. Curtis Eaves & Arthur F. Veinott, 2014. "Maximum-Stopping-Value Policies in Finite Markov Population Decision Chains," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 597-606, August.
    4. Michael O’Sullivan & Arthur F. Veinott, Jr., 2017. "Polynomial-Time Computation of Strong and n -Present-Value Optimal Policies in Markov Decision Chains," Mathematics of Operations Research, INFORMS, vol. 42(3), pages 577-598, August.
    5. Maria Gonzalez-Lima & Hua Wei & Henry Wolkowicz, 2009. "A stable primal–dual approach for linear programming under nondegeneracy assumptions," Computational Optimization and Applications, Springer, vol. 44(2), pages 213-247, 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:inm:ormnsc:v:42:y:1996:i:12:p:1719-1731. 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.