Approximation of Minimal Functions by Extreme Functions
This resolves an open theoretical question in integer programming for researchers studying the Gomory-Johnson model.
The paper proves that for any n-dimensional Gomory-Johnson infinite group relaxation, every continuous minimal function can be arbitrarily well approximated by an extreme function, resolving an open question.
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.