Depth-Optimized Convexity Cuts

Jonathan Eckstein () and Mikhail Nediak ()

Annals of Operations Research, 2005, vol. 139, issue 1, 95-129

Abstract: 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. Copyright Springer Science + Business Media, Inc. 2005

Keywords: integer programming; cutting planes; convexity cuts (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10479-005-3445-y

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