On the notions of facets, weak facets, and extreme functions of the Gomory-Johnson infinite group problem

2016/11/21 by Matthias Köppe, Yuan Zhou · 1 citation
Mathematics · #math.OC #msc:90C10

paper · pdf · doi:10.1007/978-3-319-59250-3_27

published as Proc. IPCO 2017, LNCS 10328, pp. 330--342 · 18 pages, 2 figures

arxiv created 2016/11/21 · arxiv updated 2017/07/13

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 then separate the three notions using discontinuous examples.

Cited by

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