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International Conference on Integer Programming and Combinatorial Optimization

IPCO 2010: Integer Programming and Combinatorial Optimization pp 124–134Cite as

A Polyhedral Study of the Mixed Integer Cut

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6080))

Abstract

General purpose cutting planes have played a central role in modern IP solvers. In practice, the Gomory mixed integer cut has proven to be among the most useful general purpose cuts. One may obtain this inequality from the group relaxation of an IP, which arises by relaxing non-negativity on the basic variables. We study the mixed integer cut as a facet of the master cyclic group polyhedron and characterize its extreme points and adjacent facets in this setting. Extensions are provided under automorphic and homomorphic mappings.

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References

  1. Aráoz, J., Evans, L., Gomory, R.E., Johnson, E.L.: Cyclic group and knapsack facets. Math. Program. 96(2), 377–408 (2003)

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  2. Dash, S., Günlük, O.: On the strength of gomory mixed-integer cuts as group cuts. Math. Program. 115(2), 387–407 (2008)

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  3. Gomory, R.E.: Some polyhedra related to combinatorial problems. Linear Algebra and Its Applications (2), 451–558 (1969)

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  4. Gomory, R.E., Johnson, E.L., Evans, L.: Corner polyhedra and their connection with cutting planes. Math. Program. 96(2), 321–339 (2003)

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Author information

Authors and Affiliations

  1. H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    Steve Tyber & Ellis L. Johnson

Authors
  1. Steve Tyber
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  2. Ellis L. Johnson
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Editor information

Editors and Affiliations

  1. Institute of Mathematics, École Polytechnique Féderale de Lausanne, 1015, Lausanne, Switzerland

    Friedrich Eisenbrand

  2. McGill University, 805 Sherbrooke West, H3A 2K6, Montreal, Quebec, Canada

    F. Bruce Shepherd

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© 2010 Springer-Verlag Berlin Heidelberg

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Tyber, S., Johnson, E.L. (2010). A Polyhedral Study of the Mixed Integer Cut. In: Eisenbrand, F., Shepherd, F.B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2010. Lecture Notes in Computer Science, vol 6080. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13036-6_10

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  • DOI: https://doi.org/10.1007/978-3-642-13036-6_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13035-9

  • Online ISBN: 978-3-642-13036-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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