Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. VI. The curious case of two-sided discontinuous minimal valid functions

TL;DR

This paper constructs a novel two-sided discontinuous minimal valid function for the Gomory-Johnson model that is not extreme nor a convex combination of others, and introduces an algorithm for related perturbations.

Contribution

It presents a new class of discontinuous minimal valid functions and an algorithm for their perturbations, advancing understanding of the Gomory-Johnson model.

Findings

Constructed a two-sided discontinuous minimal valid function.

Showed the function is not extreme and not a convex combination.

Developed an algorithm for microperiodic perturbations.

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. The new function only admits piecewise microperiodic perturbations. We present an algorithm for computations with a restricted class of such perturbations.