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Technical Note—Facets and Strong Valid Inequalities for Integer Programs

Author

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  • Laurence A. Wolsey

    (Center for Operations Research and Econometrics, Louvain, Belgium)

Abstract

We give a general result showing when a valid inequality or facet of an integer polytope can be obtained from a valid inequality or facet in a subset of the variables.

Suggested Citation

  • Laurence A. Wolsey, 1976. "Technical Note—Facets and Strong Valid Inequalities for Integer Programs," Operations Research, INFORMS, vol. 24(2), pages 367-372, April.
    • Handle: RePEc:inm:oropre:v:24:y:1976:i:2:p:367-372
    DOI: 10.1287/opre.24.2.367
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    Cited by:

    1. Pasquale Avella & Maurizio Boccia & Igor Vasilyev, 2012. "Computational Testing of a Separation Procedure for the Knapsack Set with a Single Continuous Variable," INFORMS Journal on Computing, INFORMS, vol. 24(1), pages 165-171, February.
    2. Manfred Padberg, 2005. "Classical Cuts for Mixed-Integer Programming and Branch-and-Cut," Annals of Operations Research, Springer, vol. 139(1), pages 321-352, October.
    3. Alper Atamtürk, 2004. "Sequence Independent Lifting for Mixed-Integer Programming," Operations Research, INFORMS, vol. 52(3), pages 487-490, June.
    4. 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.
    5. Giovanni Felici & Claudio Gentile, 2003. "Zero-Lifting for Integer Block Structured Problems," Journal of Combinatorial Optimization, Springer, vol. 7(2), pages 161-167, June.
    6. Robert E. Bixby & Eva K. Lee, 1998. "Solving a Truck Dispatching Scheduling Problem Using Branch-and-Cut," Operations Research, INFORMS, vol. 46(3), pages 355-367, June.
    7. Santanu S. Dey & Jean-Philippe Richard, 2009. "Linear-Programming-Based Lifting and Its Application to Primal Cutting-Plane Algorithms," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 137-150, February.
    8. Xiaoyi Gu & Santanu S. Dey & Jean-Philippe P. Richard, 2024. "Solving Sparse Separable Bilinear Programs Using Lifted Bilinear Cover Inequalities," INFORMS Journal on Computing, INFORMS, vol. 36(3), pages 884-899, May.
    9. Amar K. Narisetty & Jean-Philippe P. Richard & George L. Nemhauser, 2011. "Lifted Tableaux Inequalities for 0--1 Mixed-Integer Programs: A Computational Study," INFORMS Journal on Computing, INFORMS, vol. 23(3), pages 416-424, August.
    10. Alper Atamtürk, 2005. "Cover and Pack Inequalities for (Mixed) Integer Programming," Annals of Operations Research, Springer, vol. 139(1), pages 21-38, October.
    11. I. R. De Farias & E. L. Johnson & G. L. Nemhauser, 2002. "Facets of the Complementarity Knapsack Polytope," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 210-226, February.
    12. Wei-Kun Chen & Liang Chen & Yu-Hong Dai, 2023. "Lifting for the integer knapsack cover polyhedron," Journal of Global Optimization, Springer, vol. 86(1), pages 205-249, May.
    13. Zonghao Gu & George L. Nemhauser & Martin W.P. Savelsbergh, 2000. "Sequence Independent Lifting in Mixed Integer Programming," Journal of Combinatorial Optimization, Springer, vol. 4(1), pages 109-129, March.
    14. Quentin Louveaux & Laurence Wolsey, 2007. "Lifting, superadditivity, mixed integer rounding and single node flow sets revisited," Annals of Operations Research, Springer, vol. 153(1), pages 47-77, September.

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