Abstract
The infinite models in integer programming can be described as the convex hull of some points or as the intersection of halfspaces derived from valid functions. In this paper we study the relationships between these two descriptions. Our results have implications for finite dimensional corner polyhedra. One consequence is that nonnegative continuous functions suffice to describe finite dimensional corner polyhedra with rational data. We also discover new facts about corner polyhedra with non-rational data.
A. Basu and J. Paat—Supported by the NSF grant CMMI1452820.
M. Conforti and M. Di Summa—Supported by the grant “Progetto di Ateneo 2013”.
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Notes
- 1.
Such results are obtainable in the case \(n=1\) by more elementary means such as interpolation. We are unaware of a way to establish these results for general \(n\ge 2\) without using the technology developed in this paper.
- 2.
For an explicit construction of such a function, see the journal version of the paper.
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Basu, A., Conforti, M., Di Summa, M., Paat, J. (2017). The Structure of the Infinite Models in Integer Programming. In: Eisenbrand, F., Koenemann, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 2017. Lecture Notes in Computer Science(), vol 10328. Springer, Cham. https://doi.org/10.1007/978-3-319-59250-3_6
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