Approximation of Minimal Functions by Extreme Functions

Abstract

In a recent paper, Basu, Hildebrand, and Molinaro established that the set of continuous minimal functions for the 1-dimensional Gomory--Johnson infinite group relaxation possesses a dense subset of extreme functions. The $n$-dimensional version of this result was left as an open question. In the present paper, we settle this query in the affirmative: for any integer $n \geq 1$, every continuous minimal function can be arbitrarily well approximated by an extreme function in the $n$-dimensional Gomory--Johnson model.