Mathematical Programming

, Volume 137, Issue 1–2, pp 19–35

Generalized intersection cuts and a new cut generating paradigm

Full Length Paper Series A

DOI: 10.1007/s10107-011-0483-x

Cite this article as:
Balas, E. & Margot, F. Math. Program. (2013) 137: 19. doi:10.1007/s10107-011-0483-x


Intersection cuts are generated from a polyhedral cone and a convex set S whose interior contains no feasible integer point. We generalize these cuts by replacing the cone with a more general polyhedron C. The resulting generalized intersection cuts dominate the original ones. This leads to a new cutting plane paradigm under which one generates and stores the intersection points of the extreme rays of C with the boundary of S rather than the cuts themselves. These intersection points can then be used to generate in a non-recursive fashion cuts that would require several recursive applications of some standard cut generating routine. A procedure is also given for strengthening the coefficients of the integer-constrained variables of a generalized intersection cut. The new cutting plane paradigm yields a new characterization of the closure of intersection cuts and their strengthened variants. This characterization is minimal in the sense that every one of the inequalities it uses defines a facet of the closure.

Mathematics Subject Classification (2000)

90C10 90C11 90C57 

Copyright information

© Springer and Mathematical Optimization Society 2011

Authors and Affiliations

  1. 1.Tepper School of Business, Carnegie Mellon UniversityPittsburghUSA

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