IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v49y2011i4p623-649.html
   My bibliography  Save this article

Branching on hyperplane methods for mixed integer linear and convex programming using adjoint lattices

Author

Listed:
  • Sanjay Mehrotra
  • Zhifeng Li

Abstract

No abstract is available for this item.

Suggested Citation

  • Sanjay Mehrotra & Zhifeng Li, 2011. "Branching on hyperplane methods for mixed integer linear and convex programming using adjoint lattices," Journal of Global Optimization, Springer, vol. 49(4), pages 623-649, April.
    • Handle: RePEc:spr:jglopt:v:49:y:2011:i:4:p:623-649
    DOI: 10.1007/s10898-010-9554-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-010-9554-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-010-9554-4?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Herbert E. Scarf & Laszlo Lovasz, 1990. "The Generalized Basis Reduction Algorithm," Cowles Foundation Discussion Papers 946, Cowles Foundation for Research in Economics, Yale University.
    2. Karen Aardal & Arjen K. Lenstra, 2004. "Hard Equality Constrained Integer Knapsacks," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 724-738, August.
    3. Leonid G. Khachiyan, 1996. "Rounding of Polytopes in the Real Number Model of Computation," Mathematics of Operations Research, INFORMS, vol. 21(2), pages 307-320, May.
    4. H. W. Lenstra, 1983. "Integer Programming with a Fixed Number of Variables," Mathematics of Operations Research, INFORMS, vol. 8(4), pages 538-548, November.
    5. ANSTREICHER, Kurt M., 1999. "Ellipsoidal approximations of convex sets based on the volumetric barrier," LIDAM Reprints CORE 1393, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. William Cook & Thomas Rutherford & Herbert E. Scarf & David Shallcross, 1993. "An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 5(2), pages 206-212, May.
    7. AARDAL, Karen & WEISMANTEL, Robert & WOLSEY, Laurence, 2002. "Non-standard approaches to integer programming," LIDAM Reprints CORE 1568, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. K. M. Anstreicher, 1999. "Ellipsoidal Approximations of Convex Sets Based on the Volumetric Barrier," Mathematics of Operations Research, INFORMS, vol. 24(1), pages 193-203, February.
    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. Kibaek Kim & Sanjay Mehrotra, 2015. "A Two-Stage Stochastic Integer Programming Approach to Integrated Staffing and Scheduling with Application to Nurse Management," Operations Research, INFORMS, vol. 63(6), pages 1431-1451, December.
    2. Miguel Anjos & Xiao-Wen Chang & Wen-Yang Ku, 2014. "Lattice preconditioning for the real relaxation branch-and-bound approach for integer least squares problems," Journal of Global Optimization, Springer, vol. 59(2), pages 227-242, July.
    3. Karen Aardal & Frederik von Heymann, 2014. "On the Structure of Reduced Kernel Lattice Bases," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 823-840, August.

    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. Karen Aardal & Frederik von Heymann, 2014. "On the Structure of Reduced Kernel Lattice Bases," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 823-840, August.
    2. Elhedhli, Samir & Naoum-Sawaya, Joe, 2015. "Improved branching disjunctions for branch-and-bound: An analytic center approach," European Journal of Operational Research, Elsevier, vol. 247(1), pages 37-45.
    3. Karen Aardal & Cor A. J. Hurkens & Arjen K. Lenstra, 2000. "Solving a System of Linear Diophantine Equations with Lower and Upper Bounds on the Variables," Mathematics of Operations Research, INFORMS, vol. 25(3), pages 427-442, August.
    4. Gérard Cornuéjols & Milind Dawande, 1999. "A Class of Hard Small 0-1 Programs," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 205-210, May.
    5. Kurt M. Anstreicher, 2000. "The Volumetric Barrier for Semidefinite Programming," Mathematics of Operations Research, INFORMS, vol. 25(3), pages 365-380, August.
    6. Thorsten Koch & Ted Ralphs & Yuji Shinano, 2012. "Could we use a million cores to solve an integer program?," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(1), pages 67-93, August.
    7. William Cook & Thomas Rutherford & Herbert E. Scarf & David F. Shallcross, 1991. "An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming," Cowles Foundation Discussion Papers 990, Cowles Foundation for Research in Economics, Yale University.
    8. Karen Aardal & Arjen K. Lenstra, 2004. "Hard Equality Constrained Integer Knapsacks," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 724-738, August.
    9. Yu Yang & Natashia Boland & Martin Savelsbergh, 2021. "Multivariable Branching: A 0-1 Knapsack Problem Case Study," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1354-1367, October.
    10. Miguel Anjos & Xiao-Wen Chang & Wen-Yang Ku, 2014. "Lattice preconditioning for the real relaxation branch-and-bound approach for integer least squares problems," Journal of Global Optimization, Springer, vol. 59(2), pages 227-242, July.
    11. K. Aardal & R. E. Bixby & C. A. J. Hurkens & A. K. Lenstra & J. W. Smeltink, 2000. "Market Split and Basis Reduction: Towards a Solution of the Cornuéjols-Dawande Instances," INFORMS Journal on Computing, INFORMS, vol. 12(3), pages 192-202, August.
    12. Alberto Del Pia & Robert Hildebrand & Robert Weismantel & Kevin Zemmer, 2016. "Minimizing Cubic and Homogeneous Polynomials over Integers in the Plane," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 511-530, May.
    13. Friedrich Eisenbrand & Gennady Shmonin, 2008. "Parametric Integer Programming in Fixed Dimension," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 839-850, November.
    14. Masing, Berenike & Lindner, Niels & Borndörfer, Ralf, 2022. "The price of symmetric line plans in the Parametric City," Transportation Research Part B: Methodological, Elsevier, vol. 166(C), pages 419-443.
    15. Selin Ahipaşaoğlu, 2015. "Fast algorithms for the minimum volume estimator," Journal of Global Optimization, Springer, vol. 62(2), pages 351-370, June.
    16. Danny Nguyen & Igor Pak, 2020. "The Computational Complexity of Integer Programming with Alternations," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 191-204, February.
    17. Sascha Kurz & Nikolas Tautenhahn, 2013. "On Dedekind’s problem for complete simple games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 411-437, May.
    18. Elizabeth Baldwin & Paul Klemperer, 2019. "Understanding Preferences: “Demand Types”, and the Existence of Equilibrium With Indivisibilities," Econometrica, Econometric Society, vol. 87(3), pages 867-932, May.
    19. Herbert E. Scarf & David F. Shallcross, 2008. "The Frobenius Problem and Maximal Lattice Free Bodies," Palgrave Macmillan Books, in: Zaifu Yang (ed.), Herbert Scarf’s Contributions to Economics, Game Theory and Operations Research, chapter 7, pages 149-153, Palgrave Macmillan.
    20. Mauro Dell’Amico & Simone Falavigna & Manuel Iori, 2015. "Optimization of a Real-World Auto-Carrier Transportation Problem," Transportation Science, INFORMS, vol. 49(2), pages 402-419, May.

    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:spr:jglopt:v:49:y:2011:i:4:p:623-649. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.