Non-unique lifting of integer variables in minimal inequalities

TL;DR

This paper develops a general theory for lifting in cut-generating functions, especially focusing on cases without the unique lifting property, expanding understanding beyond prior work.

Contribution

It introduces a comprehensive framework for analyzing lifting in cut-generating functions lacking the unique lifting property, filling a gap in existing literature.

Findings

Established a general theory for non-unique lifting scenarios

Extended the understanding of cut-generating functions beyond unique lifting cases

Provided new insights into the structure of minimal inequalities

Abstract

We explore the lifting question in the context of cut-generating functions. Most of the prior literature on this question focuses on cut-generating functions that have the unique lifting property. We develop a general theory for understanding the lifting question for cut-generating functions that do not necessarily have the unique lifting property.