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

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

2011-09-19

arxiv.org/abs/1109.4184v1

Mathematics

Optimization and Control

25 pages, 2 figures

Scientific paper

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 Cornuejols and Molinaro for k=2.

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