Mathematical Programming

, Volume 94, Issue 2–3, pp 193–206 | Cite as

Integral decomposition of polyhedra and some applications in mixed integer programming

  • Martin Henk
  • Matthias Köppe
  • Robert Weismantel

Abstract.

 This paper addresses the question of decomposing an infinite family of rational polyhedra in an integer fashion. It is shown that there is a finite subset of this family that generates the entire family. Moreover, an integer analogue of Carathéodory's theorem carries over to this general setting. The integer decomposition of a family of polyhedra has some applications in integer and mixed integer programming, including a test set approach to mixed integer programming.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Martin Henk
    • 1
  • Matthias Köppe
    • 1
  • Robert Weismantel
    • 1
  1. 1.Department of Mathematics/IMO, University of Magdeburg, Universitätsplatz 2, D-39106 Magdeburg, e-mail: {henk, mkoeppe, weismantel}@imo.math.uni-magdeburg.deDE

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