A New Algebraic Geometry Algorithm for Integer Programming

  • Authors:

  • Dimitris Bertsimas;Georgia Perakis;Sridhar Tayur

  • Affiliations:

  • -;-;-

  • Venue:
  • Management Science
  • Year:
  • 2000

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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.