Intersection Disjunctions for Reverse Convex Sets

Eli Towle () and James Luedtke ()
Additional contact information
Eli Towle: Department of Industrial and Systems Engineering, University of Wisconsin–Madison, Madison, Wisconsin 53706
James Luedtke: Department of Industrial and Systems Engineering, University of Wisconsin–Madison, Madison, Wisconsin 53706

Mathematics of Operations Research, 2022, vol. 47, issue 1, 297-319

Abstract: We present a framework to obtain valid inequalities for a reverse convex set: the set of points in a polyhedron that lie outside a given open convex set. Reverse convex sets arise in many models, including bilevel optimization and polynomial optimization. An intersection cut is a well-known valid inequality for a reverse convex set that is generated from a basic solution that lies within the convex set. We introduce a framework for deriving valid inequalities for the reverse convex set from basic solutions that lie outside the convex set. We first propose an extension to intersection cuts that defines a two-term disjunction for a reverse convex set, which we refer to as an intersection disjunction. Next, we generalize this analysis to a multiterm disjunction by considering the convex set’s recession directions. These disjunctions can be used in a cut-generating linear program to obtain valid inequalities for the reverse convex set.

Keywords: Primary: 90C11; secondary: 90C26; 90C10; mixed-integer nonlinear programming; valid inequalities; reverse convex sets; disjunctive programming; intersection cuts; concavity cuts (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
http://dx.doi.org/10.1287/moor.2021.1132 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:47:y:2022:i:1:p:297-319

Access Statistics for this article

More articles in Mathematics of Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().