Facets, weak facets, and extreme functions of the Gomory–Johnson infinite group problem

Matthias Köppe, Yuan Zhou

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)195-252
Number of pages58
JournalMathematical Programming
Volume187
Issue number1-2
DOIs
StatePublished - May 2021

Bibliographical note

Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society.

ASJC Scopus subject areas

  • Software
  • General Mathematics

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