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A New Algebraic Geometry Algorithm for Integer Programming

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Author Info

  • Dimitris Bertsimas

    (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Georgia Perakis

    (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Sridhar Tayur

    (Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

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    Abstract

    We propose a new algorithm for solving integer programming (IP) problems that is based on ideas from algebraic geometry. The method provides a natural generalization of the Farkas lemma for IP, leads to a way of performing sensitivity analysis, offers a systematic enumeration of all feasible solutions, and gives structural information of the feasible set of a given IP. We provide several examples that offer insights on the algorithm and its properties.

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    File URL: http://dx.doi.org/10.1287/mnsc.46.7.999.12033
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 46 (2000)
    Issue (Month): 7 (July)
    Pages: 999-1008

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    Handle: RePEc:inm:ormnsc:v:46:y:2000:i:7:p:999-1008

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    Related research

    Keywords: integer programming; algebraic geometry; Groebner basis;

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    Cited by:
    1. Castro, F. & Gago, J. & Hartillo, I. & Puerto, J. & Ucha, J.M., 2011. "An algebraic approach to integer portfolio problems," European Journal of Operational Research, Elsevier, vol. 210(3), pages 647-659, May.

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