IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v52y2004i3p487-490.html
   My bibliography  Save this article

Sequence Independent Lifting for Mixed-Integer Programming

Author

Listed:
  • Alper Atamtürk

    (Department of Industrial Engineering and Operations Research, University of California at Berkeley, Berkeley, California 94720-1777)

Abstract

We show that superadditive lifting functions lead to sequence independent lifting of inequalities for general mixed-integer programming. As an application, we note that mixed-integer rounding (MIR) may be viewed as sequence independent lifting. Consequently, we obtain facet conditions for MIR inequalities for mixed-integer knapsacks.

Suggested Citation

  • Alper Atamtürk, 2004. "Sequence Independent Lifting for Mixed-Integer Programming," Operations Research, INFORMS, vol. 52(3), pages 487-490, June.
  • Handle: RePEc:inm:oropre:v:52:y:2004:i:3:p:487-490
    DOI: 10.1287/opre.1030.0099
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1030.0099
    Download Restriction: no

    File URL: https://libkey.io/10.1287/opre.1030.0099?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. WOLSEY, Laurence A., 1977. "Valid inequalities and superadditivity for 0-1 integer programs," LIDAM Reprints CORE 328, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. MARCHAND, Hugues & WOLSEY, Laurence A., 2001. "Aggregation and mixed integer rounding to solve mips," LIDAM Reprints CORE 1513, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. L. A. Wolsey, 1977. "Valid Inequalities and Superadditivity for 0--1 Integer Programs," Mathematics of Operations Research, INFORMS, vol. 2(1), pages 66-77, February.
    4. Laurence A. Wolsey, 1976. "Technical Note—Facets and Strong Valid Inequalities for Integer Programs," Operations Research, INFORMS, vol. 24(2), pages 367-372, April.
    5. Hugues Marchand & Laurence A. Wolsey, 2001. "Aggregation and Mixed Integer Rounding to Solve MIPs," Operations Research, INFORMS, vol. 49(3), pages 363-371, June.
    6. NEMHAUSER, George L. & WOLSEY, Laurence A., 1990. "A recursive procedure to generate all cuts for 0-1 mixed integer programs," LIDAM Reprints CORE 894, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. 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.
    8. Gérard Cornuéjols & Yanjun Li & Dieter Vandenbussche, 2003. "K-Cuts: A Variation of Gomory Mixed Integer Cuts from the LP Tableau," INFORMS Journal on Computing, INFORMS, vol. 15(4), pages 385-396, November.
    9. WOLSEY, Laurence A., 1976. "Facets and strong valid inequalities for integer programs," LIDAM Reprints CORE 246, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alper Atamtürk, 2005. "Cover and Pack Inequalities for (Mixed) Integer Programming," Annals of Operations Research, Springer, vol. 139(1), pages 21-38, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. Alper Atamtürk, 2005. "Cover and Pack Inequalities for (Mixed) Integer Programming," Annals of Operations Research, Springer, vol. 139(1), pages 21-38, October.
    5. 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.
    6. 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.
    7. 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.
    8. Amitabh Basu & Pierre Bonami & Gérard Cornuéjols & François Margot, 2011. "Experiments with Two-Row Cuts from Degenerate Tableaux," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 578-590, November.
    9. Michele Conforti & Gérard Cornuéjols & Giacomo Zambelli, 2011. "A Geometric Perspective on Lifting," Operations Research, INFORMS, vol. 59(3), pages 569-577, June.
    10. Christopher Hojny & Tristan Gally & Oliver Habeck & Hendrik Lüthen & Frederic Matter & Marc E. Pfetsch & Andreas Schmitt, 2020. "Knapsack polytopes: a survey," Annals of Operations Research, Springer, vol. 292(1), pages 469-517, September.
    11. Andreas Eisenblätter & Hans-Florian Geerdes & Thorsten Koch & Alexander Martin & Roland Wessäly, 2006. "UMTS radio network evaluation and optimization beyond snapshots," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(1), pages 1-29, February.
    12. 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.
    13. William Cook & Sanjeeb Dash & Ricardo Fukasawa & Marcos Goycoolea, 2009. "Numerically Safe Gomory Mixed-Integer Cuts," INFORMS Journal on Computing, INFORMS, vol. 21(4), pages 641-649, November.
    14. Alper Atamtürk & Martin Savelsbergh, 2005. "Integer-Programming Software Systems," Annals of Operations Research, Springer, vol. 140(1), pages 67-124, November.
    15. 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.
    16. 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.
    17. Matteo Fischetti & Domenico Salvagnin, 2013. "Approximating the Split Closure," INFORMS Journal on Computing, INFORMS, vol. 25(4), pages 808-819, November.
    18. Absi, Nabil & Kedad-Sidhoum, Safia, 2008. "The multi-item capacitated lot-sizing problem with setup times and shortage costs," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1351-1374, March.
    19. Sanjeeb Dash & Marcos Goycoolea & Oktay Günlük, 2010. "Two-Step MIR Inequalities for Mixed Integer Programs," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 236-249, May.
    20. Santanu S. Dey & Jean-Philippe P. Richard, 2008. "Facets of Two-Dimensional Infinite Group Problems," Mathematics of Operations Research, INFORMS, vol. 33(1), pages 140-166, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:52:y:2004:i:3:p:487-490. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.