Facets, weak facets, and extreme functions of the Gomory-Johnson infinite group problem
Optimization and Control
2019-11-15 v1
Abstract
We investigate three competing notions that generalize the notion of a facet of finite-dimensional polyhedra to the infinite-dimensional Gomory-Johnson model. These notions were known to coincide for continuous piecewise linear functions with rational breakpoints. We show that two of the notions, extreme functions and facets, coincide for the case of continuous piecewise linear functions, removing the hypothesis regarding rational breakpoints. We prove an if-and-only-if version of the Gomory-Johnson Facet Theorem. Finally, we separate the three notions using discontinuous examples.
Keywords
Cite
@article{arxiv.1911.06199,
title = {Facets, weak facets, and extreme functions of the Gomory-Johnson infinite group problem},
author = {Matthias Köppe and Yuan Zhou},
journal= {arXiv preprint arXiv:1911.06199},
year = {2019}
}
Comments
25+32 pages, 5 figures. Journal version of published extended abstract arXiv:1611.06626