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On Cutting Planes

Author

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  • Schrijver, A

Abstract

We give a geometrical description of Chvatal's version of Gomory's cutting plane method. Restricting ourselves to rational spaces, we prove that the derived geometrical objects are polyhedra again, and that the method also works for unbounded polyhedra.

Suggested Citation

  • Schrijver, A, 1980. "On Cutting Planes," University of Amsterdam, Actuarial Science and Econometrics Archive 293054, University of Amsterdam, Faculty of Economics and Business.
    • Handle: RePEc:ags:amstas:293054
    DOI: 10.22004/ag.econ.293054
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    Cited by:

    1. Alexander Razborov, 2017. "On the Width of Semialgebraic Proofs and Algorithms," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1106-1134, November.
    2. Aardal, K.I. & van Hoesel, S., 1995. "Polyhedral Techniques in Combinatorial Optimization," Other publications TiSEM ed028a07-eb6a-4c8d-8f21-d, Tilburg University, School of Economics and Management.
    3. Alberto Del Pia & Robert Weismantel, 2016. "Relaxations of mixed integer sets from lattice-free polyhedra," Annals of Operations Research, Springer, vol. 240(1), pages 95-117, May.
    4. Thomas Rothvoß & Laura Sanità, 2017. "0/1 Polytopes with Quadratic Chvátal Rank," Operations Research, INFORMS, vol. 65(1), pages 212-220, February.
    5. William Cook & Sanjeeb Dash, 2001. "On the Matrix-Cut Rank of Polyhedra," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 19-30, February.
    6. Alexander Bockmayr & Friedrich Eisenbrand, 2001. "Cutting Planes and the Elementary Closure in Fixed Dimension," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 304-312, May.
    7. Juliane Dunkel & Andreas S. Schulz, 2013. "The Gomory-Chvátal Closure of a Nonrational Polytope Is a Rational Polytope," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 63-91, February.
    8. Thomas Rothvoß & Laura Sanità, 2017. "0/1 Polytopes with Quadratic Chvátal Rank," Operations Research, INFORMS, vol. 65(1), pages 212-220, February.
    9. Aardal, K.I. & van Hoesel, S., 1995. "Polyhedral Techniques in Combinatorial Optimization," Discussion Paper 1995-57, Tilburg University, Center for Economic Research.
    10. Daniel Dadush & Santanu S. Dey & Juan Pablo Vielma, 2011. "The Chvátal-Gomory Closure of a Strictly Convex Body," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 227-239, May.
    11. Aardal, K. & van Hoesel, C.P.M., 1995. "Polyhedral techniques in combinatorial optimization," Research Memorandum 014, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    12. Sanjeeb Dash, 2005. "Exponential Lower Bounds on the Lengths of Some Classes of Branch-and-Cut Proofs," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 678-700, August.

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