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

• 成果类型: Article
• 署名作者: Koppe, Matthias; Zhou, Yuan
• 署名单位: University of California System; University of California Davis; University of Kentucky
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-020-01477-2
• 发表日期: 2021
• 页码: 195-252
• 关键词: equivariant perturbation; FOUNDATIONS; light

摘要

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.