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The omnipresence of Lagrange

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  • 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
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    References listed on IDEAS

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    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. 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.
    3. Marshall L. Fisher, 1973. "Optimal Solution of Scheduling Problems Using Lagrange Multipliers: Part I," Operations Research, INFORMS, vol. 21(5), pages 1114-1127, October.
    4. 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.
    5. Richard C. Grinold, 1970. "Lagrangian Subgradients," Management Science, INFORMS, vol. 17(3), pages 185-188, November.
    6. 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.
    7. 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.
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