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The omnipresence of Lagrange

Research paper by Claude Lemaréchal

Indexed on: 17 May '07Published on: 17 May '07Published in: Annals of Operations Research



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).