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The omnipresence of Lagrange

Research paper by Claude Lemaréchal

Indexed on: 01 Mar '03Published on: 01 Mar '03Published in: 4OR



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).