Cet ouvrage traite de la M�thode des Multiplicateurs de Lagrange, qui est l'une des techniques les plus efficaces de l'Optimisation Diff�rentiable et/ou Convexe. Cette derni�re est elle-m�me l'une des branches les plus �labor�es de l'Optimisation et s'occupe de la minimisation de fonctions objectif diff�rentiables ou convexes ayant des variables qui sont contraintes � d�crire des surfaces diff�rentiables ou des ensembles convexes non ouverts avec bords emp�chant l'application du th�or�me classique d'Euler. Mais, gr�ce � l'introduction du multiplicateur de Lagrange, on peut par exemple transformer un probl�me d'optimisation diff�rentiable de fonction objectif F avec contrainte d'�galit� {G(x)=0} en un probl�me d'optimisation globale de la fonction lagrangienne L d�finie par L(x,λ)=F(x)+λ�G(x). Un tel param�tre λ est le multiplicateur de Lagrange ou la variable duale et peut �tre un r�el, un n-uplet de r�els, ou une forme lin�aire continue suivant que G soit � valeurs dans IR, IRⁿ ou dans un espace de fonctions. Les domaines d'application s'�tendent au Contr�le Optimal (Recherche Op�rationnelle), � la T�l�communication, aux Probl�mes de Contact et de Friction, etc...

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