Operations that preserve the covering property of the lifting region

TL;DR

This paper introduces three new operations that preserve the covering property of structured cut-generating functions, significantly expanding the set of usable functions in computational optimization.

Contribution

It provides novel operations that maintain the covering property, generalizing previous results with new proof techniques for future research.

Findings

Expanded the set of undominated cut-generating functions available for computation

Generalized previous results on operations preserving the covering property

Introduced new proof techniques suitable for future research

Abstract

We contribute to the theory for minimal liftings of cut-generating functions. In particular, we give three operations that preserve the so-called covering property of certain structured cut-generating functions. This has the consequence of vastly expanding the set of undominated cut generating functions which can be used computationally, compared to known examples from the literature. The results of this paper are significant generalizations of previous results from the literature on such operations, and also use completely different proof techniques which we feel are more suitable for attacking future research questions in this area.