Skip to main content
Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. VI. The
Curious Case of Two-Sided Discontinuous Functions
Published Web Location
https://arxiv.org/pdf/1605.03975.pdfNo data is associated with this publication.
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.