Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. VI. The Curious Case of Two-Sided Discontinuous Functions
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Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. VI. The Curious Case of Two-Sided Discontinuous Functions

  • Author(s): Köppe, Matthias
  • Zhou, Yuan
  • et al.

Published Web Location

https://arxiv.org/pdf/1605.03975.pdf
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Abstract

We construct a two-sided discontinuous piecewise linear minimal valid function for the 1-row Gomory--Johnson model which is not extreme, but which is not a convex combination of other piecewise linear minimal valid functions. This anomalous behavior results from combining features of Hildebrand's two-sided discontinuous extreme functions and Basu--Hildebrand--K\"{o}ppe's piecewise linear extreme function with irrational breakpoints. The new function only admits piecewise microperiodic perturbations. We present an algorithm for computations with a restricted class of such perturbations.

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