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 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 computations with a restricted class of such perturbations. 
Matthias K\"oppe and Yuan Zhou
math.OC