Le but de cet ouvrage est de pr�senter une m�thode de recherche d'un minimum d'une fonction convexe, propre et semi-continue inf�rieurement; c'est-�-dire, une m�thode de recherche d'un z�ro du sous-diff�rentiel d'une fonction convexe, propre et semi-continue inf�rieurement. Il s'agit de la M�thode du Point Proximal qui est plus g�n�ralement bas�e sur un Algorithme it�ratif du calcul d'un z�ro d'un op�rateur monotone maximal, et qui a �t� introduite par Martinet en 1970 et d�velopp�e par des math�maticiens comme Rockafellar, G�ler, etc... Pour se faire, nous avons d'abord rappeler les notions essentielles de l'Optimisation Convexe et les crit�res d'existence de solutions en optimisation convexe et/ou Diff�rentiable, et ensuite exposer le fondement th�orique de la M�thode du Point Proximal pouvant �tre aussi consid�r�e comme une m�thode de r�gularisation. De plus une adaptation de l'Algorithme Proximal au cas (non convexe) d'une diff�rence de fonctions convexes, due � Sun-Sampaio-Candido, a �t� abord�e.

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PhD en Analyse Fonctionnelle et Applications, SISSA Trieste, Italie. Enseignant-Chercheur � l'Institut de Math�matiques et de Sciences Physiques (IMSP), Benin. Chercheur Associ� � l'ICTP, Trieste, Italie et � l'AUST, Abuja, Nigeria. Laur�at du Prix TWAS-CBRST 2007. Projet en collaboration avec D. Gandonou (IMSP)

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