Annals of Operations Research

, Volume 139, Issue 1, pp 95–129 | Cite as

Depth-Optimized Convexity Cuts

  • Jonathan Eckstein
  • Mikhail Nediak


This paper presents a general, self-contained treatment of convexity or intersection cuts. It describes two equivalent ways of generating a cut—via a convex set or a concave function—and a partial-order notion of cut strength. We then characterize the structure of the sets and functions that generate cuts that are strongest with respect to the partial order. Next, we specialize this analytical framework to the case of mixed-integer linear programming (MIP). For this case, we formulate two kinds of the deepest cut generation problem, via sets or via functions, and subsequently consider some special cases which are amenable to efficient computation. We conclude with computational tests of one of these procedures on a large set of MIPLIB problems.


integer programming cutting planes convexity cuts 


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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Business School and RUTCORRutgers UniversityPiscatawayUSA
  2. 2.School of BusinessQueen's UniversityKingstonCanada

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