IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v153y2007i1p9-2710.1007-s10479-007-0169-1.html
   My bibliography  Save this article

The omnipresence of Lagrange

Author

Listed:
  • Claude Lemaréchal

Abstract

Lagrangian relaxation is usually considered in the combinatorial optimization community as a mere technique, sometimes useful to compute bounds. It is actually a very general method, inevitable as soon as one bounds optimal values, relaxes constraints, convexifies sets, generates columns, etc. In this paper we review this method, from both points of view of theory (to dualize a given problem) and algorithms (to solve the dual by nonsmooth optimization). Copyright Springer Science+Business Media, LLC 2007

Suggested Citation

  • Claude Lemaréchal, 2007. "The omnipresence of Lagrange," Annals of Operations Research, Springer, vol. 153(1), pages 9-27, September.
    • Handle: RePEc:spr:annopr:v:153:y:2007:i:1:p:9-27:10.1007/s10479-007-0169-1
    DOI: 10.1007/s10479-007-0169-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-007-0169-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-007-0169-1?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. François Vanderbeck, 2000. "On Dantzig-Wolfe Decomposition in Integer Programming and ways to Perform Branching in a Branch-and-Price Algorithm," Operations Research, INFORMS, vol. 48(1), pages 111-128, February.
    2. Marshall L. Fisher, 1973. "Optimal Solution of Scheduling Problems Using Lagrange Multipliers: Part I," Operations Research, INFORMS, vol. 21(5), pages 1114-1127, October.
    3. A. Ouorou & P. Mahey & J.-Ph. Vial, 2000. "A Survey of Algorithms for Convex Multicommodity Flow Problems," Management Science, INFORMS, vol. 46(1), pages 126-147, January.
    4. Richard C. Grinold, 1970. "Lagrangian Subgradients," Management Science, INFORMS, vol. 17(3), pages 185-188, November.
    5. T. L. Magnanti & J. F. Shapiro & M. H. Wagner, 1976. "Generalized Linear Programming Solves the Dual," Management Science, INFORMS, vol. 22(11), pages 1195-1203, July.
    6. J. L. Goffin & A. Haurie & J. P. Vial, 1992. "Decomposition and Nondifferentiable Optimization with the Projective Algorithm," Management Science, INFORMS, vol. 38(2), pages 284-302, February.
    7. John A. Muckstadt & Sherri A. Koenig, 1977. "An Application of Lagrangian Relaxation to Scheduling in Power-Generation Systems," Operations Research, INFORMS, vol. 25(3), pages 387-403, June.
    Full references (including those not matched with items on IDEAS)

    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. Panagiotis Andrianesis & Dimitris Bertsimas & Michael C. Caramanis & William W. Hogan, 2020. "Computation of Convex Hull Prices in Electricity Markets with Non-Convexities using Dantzig-Wolfe Decomposition," Papers 2012.13331, arXiv.org, revised Oct 2021.
    2. F. Babonneau & O. du Merle & J.-P. Vial, 2006. "Solving Large-Scale Linear Multicommodity Flow Problems with an Active Set Strategy and Proximal-ACCPM," Operations Research, INFORMS, vol. 54(1), pages 184-197, February.
    3. Frédéric Babonneau & Jean-Philippe Vial, 2008. "An Efficient Method to Compute Traffic Assignment Problems with Elastic Demands," Transportation Science, INFORMS, vol. 42(2), pages 249-260, May.
    4. Gondzio, Jacek & González-Brevis, Pablo & Munari, Pedro, 2013. "New developments in the primal–dual column generation technique," European Journal of Operational Research, Elsevier, vol. 224(1), pages 41-51.
    5. Marshall L. Fisher, 2004. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 50(12_supple), pages 1861-1871, December.
    6. Ogbe, Emmanuel & Li, Xiang, 2017. "A new cross decomposition method for stochastic mixed-integer linear programming," European Journal of Operational Research, Elsevier, vol. 256(2), pages 487-499.
    7. Oliver Faust & Jochen Gönsch & Robert Klein, 2017. "Demand-Oriented Integrated Scheduling for Point-to-Point Airlines," Transportation Science, INFORMS, vol. 51(1), pages 196-213, February.
    8. Gürel, Sinan, 2011. "A conic quadratic formulation for a class of convex congestion functions in network flow problems," European Journal of Operational Research, Elsevier, vol. 211(2), pages 252-262, June.
    9. Amy Cohn & Michael Magazine & George Polak, 2009. "Rank‐Cluster‐and‐Prune: An algorithm for generating clusters in complex set partitioning problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(3), pages 215-225, April.
    10. Barry C. Smith & Ellis L. Johnson, 2006. "Robust Airline Fleet Assignment: Imposing Station Purity Using Station Decomposition," Transportation Science, INFORMS, vol. 40(4), pages 497-516, November.
    11. Mukherjee, Saral & Chatterjee, A.K., 2006. "The average shadow price for MILPs with integral resource availability and its relationship to the marginal unit shadow price," European Journal of Operational Research, Elsevier, vol. 169(1), pages 53-64, February.
    12. Paraskevopoulos, Dimitris C. & Gürel, Sinan & Bektaş, Tolga, 2016. "The congested multicommodity network design problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 85(C), pages 166-187.
    13. Hela Masri & Saoussen Krichen, 2018. "Exact and approximate approaches for the Pareto front generation of the single path multicommodity flow problem," Annals of Operations Research, Springer, vol. 267(1), pages 353-377, August.
    14. Yael Grushka-Cockayne & Bert De Reyck & Zeger Degraeve, 2008. "An Integrated Decision-Making Approach for Improving European Air Traffic Management," Management Science, INFORMS, vol. 54(8), pages 1395-1409, August.
    15. Krzysztof C. Kiwiel & Torbjörn Larsson & P. O. Lindberg, 2007. "Lagrangian Relaxation via Ballstep Subgradient Methods," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 669-686, August.
    16. Sung, Inkyung & Lee, Taesik, 2016. "Optimal allocation of emergency medical resources in a mass casualty incident: Patient prioritization by column generation," European Journal of Operational Research, Elsevier, vol. 252(2), pages 623-634.
    17. Daniel de Wolf & Stéphane Auray & Yves Smeers, 2015. "Using Column Generation To Solve A Coal Blending Problem," Post-Print halshs-02396784, HAL.
    18. Klose, Andreas & Gortz, Simon, 2007. "A branch-and-price algorithm for the capacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1109-1125, June.
    19. Samir Elhedhli & Jean-Louis Goffin, 2005. "Efficient Production-Distribution System Design," Management Science, INFORMS, vol. 51(7), pages 1151-1164, July.
    20. Alexander Abakumov & Svetlana Pak, 2023. "Role of Photosynthesis Processes in the Dynamics of the Plant Community," Mathematics, MDPI, vol. 11(13), pages 1-24, June.

    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:annopr:v:153:y:2007:i:1:p:9-27:10.1007/s10479-007-0169-1. 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.