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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Received: May 22, 2000 / Accepted: March 19, 2002 Published online: December 19, 2002
Key words. mixed integer programming – test sets – indecomposable polyhedra – Hilbert bases – rational polyhedral cones
This work was supported partially by the DFG through grant WE1462, by the Kultusministerium of Sachsen Anhalt through the grants FKZ37KD0099 and FKZ 2945A/0028G and by the EU Donet project ERB FMRX-CT98-0202. The first named author acknowledges the hospitality of the International Erwin Schrödinger Institute for Mathematical Physics in Vienna, where a main part of his contribution to this work has been completed.
Mathematics Subject Classification (1991): 52C17, 11H31
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Henk, M., Köppe, M. & Weismantel, R. Integral decomposition of polyhedra and some applications in mixed integer programming. Math. Program., Ser. B 94, 193–206 (2003). https://doi.org/10.1007/s10107-002-0315-0
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DOI: https://doi.org/10.1007/s10107-002-0315-0