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The structure of the infinite models in integer programming

Amitabh Basu(basu.amitabh***at***jhu.edu)
Michele Conforti(conforti***at***math.unipd.it)
Marco Di Summa(disumma***at***math.unipd.it)
Joseph Paat(jpaat1***at***jhu.edu)

Abstract: The infinite models in integer programming can be described as the convex hull of some points or as the intersection of half-spaces 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.

Keywords: cutting planes; corner polyhedron; Gomory-Johnson infinite group relaxation; mixed-integer programming

Category 1: Integer Programming ((Mixed) Integer Linear Programming )

Category 2: Integer Programming (Cutting Plane Approaches )

Category 3: Infinite Dimensional Optimization (Semi-infinite Programming )


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Entry Submitted: 12/19/2016
Entry Accepted: 12/19/2016
Entry Last Modified: 12/19/2016

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