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Lagrangian relaxation

Claude Lemarechal (claude.lemarechal***at***inrialpes.fr)

Abstract: Lagrangian relaxation is a tool to find upper bounds on a given (arbitrary) maximization problem. Sometimes, the bound is exact and an optimal solution is found. Our aim in this paper is to review this technique, the theory behind it, its numerical aspects, its relation with other techniques such as column generation.

Keywords: relaxation, lower bound, combinatorial optimization, duality, column generation, subgradient, Kelley's method, cutting plane, bundle method

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Combinatorial Optimization (Other )

Citation: in: Computational Combinatorial Optimization M. Juenger and D. Naddef (eds.) Lecture Notes in Computer Science 2241 (Springer Verlag, 2001) pp 115-160

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Entry Submitted: 03/13/2001
Entry Accepted: 03/13/2001
Entry Last Modified: 11/04/2003

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