Equivariant perturbation in Gomory and Johnson's infinite group problem. VI. The curious case of two-sided discontinuous minimal valid functions

We construct a two-sided discontinuous piecewise linear minimal valid cut-generating 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. The new function only admits piecewise microperiodic perturbations. We present an algorithm for verifying certificates of non-extremality in the form of such perturbations. (C) 2018 Elsevier B.V. All rights reserved.