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Depth-Optimized Convexity Cuts

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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.

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Authors and Affiliations

  1. Business School and RUTCOR, Rutgers University, 640 Bartholomew Road, Piscataway, NJ, 08540, USA

    Jonathan Eckstein

  2. School of Business, Queen's University, 143 Union Street, Kingston, Ontario, K7L 3N6, Canada

    Mikhail Nediak

Authors
  1. Jonathan Eckstein
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  2. Mikhail Nediak
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Correspondence to Jonathan Eckstein.

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Eckstein, J., Nediak, M. Depth-Optimized Convexity Cuts. Ann Oper Res 139, 95–129 (2005). https://doi.org/10.1007/s10479-005-3445-y

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