Depth-optimized convexity cuts

Jonathan Eckstein, Mikhail Nediak

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)95-129
Number of pages35
JournalAnnals of Operations Research
Issue number1
StatePublished - Oct 2005

All Science Journal Classification (ASJC) codes

  • Decision Sciences(all)
  • Management Science and Operations Research


  • Convexity cuts
  • Cutting planes
  • Integer programming


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