Minimal cut-generating functions are nearly extreme
Optimization and Control
2017-08-29 v2 Functional Analysis
Abstract
We study continuous (strongly) minimal cut generating functions for the model where all variables are integer. We consider both the original Gomory-Johnson setting as well as a recent extension by Cornu\'ejols and Y{\i}ld{\i}z. We show that for any continuous minimal or strongly minimal cut generating function, there exists an extreme cut generating function that approximates the (strongly) minimal function as closely as desired. In other words, the extreme functions are "dense" in the set of continuous (strongly) minimal functions.
Cite
@article{arxiv.1701.06698,
title = {Minimal cut-generating functions are nearly extreme},
author = {Amitabh Basu and Robert Hildebrand and Marco Molinaro},
journal= {arXiv preprint arXiv:1701.06698},
year = {2017}
}
Comments
A subset of these results appeared in Proceedings of IPCO 2016, Lecture Notes in Computer Science, vol. 9682, pp. 202--213