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A connection between cutting plane theory and the geometry of numbers

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Abstract.

In this paper, we relate several questions about cutting planes to a fundamental problem in the geometry of numbers, namely, the closest vector problem. Using this connection we show that the dominance, membership and validity problems are NP-complete for Chvátal and split cuts.

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Authors and Affiliations

  1. Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, USA, , , , , , US

    Gérard Cornuéjols & Yanjun Li

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  1. Gérard Cornuéjols
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  2. Yanjun Li
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Received: August 28, 2001 / Accepted: March 2002¶Published online May 8, 2002

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Cornuéjols, G., Li, Y. A connection between cutting plane theory and the geometry of numbers. Math. Program. 93, 123–127 (2002). https://doi.org/10.1007/s10107-002-0302-5

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  • DOI: https://doi.org/10.1007/s10107-002-0302-5

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