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A (k+1)-Slope Theorem for the k-Dimensional Infinite Group Relaxation

Amitabh Basu(abasu***at***math.ucdavis.edu)
Robert Hildebrand(rhildebrand***at***math.ucdavis.edu)
Matthias Koeppe(mkoeppe***at***math.ucdavis.edu)
Marco Molinaro(molinaro***at***cmu.edu)

Abstract: We prove that any minimal valid function for the k-dimensional infinite group relaxation that is piecewise linear with at most k+1 slopes and does not factor through a linear map with non-trivial kernel is extreme. This generalizes a theorem of Gomory and Johnson for k=1, and Cornu\'ejols and Molinaro for k=2.

Keywords: integer programming, infinite group relaxation, minimal valid functions, facets

Category 1: Integer Programming (Cutting Plane Approaches )

Category 2: Infinite Dimensional Optimization (Semi-infinite Programming )


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Entry Submitted: 09/19/2011
Entry Accepted: 09/20/2011
Entry Last Modified: 09/19/2011

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