Le but de cet ouvrage est de faire une pr�sentation compl�te et auto contenue de l'�quivalence entre les Oracles S�parer, Optimiser et Appartenir en Optimisation Poly�drale. Dans ce but le livre commence par une pr�sentation d�taill�e des probl�mes de Complexit� des Algorithmes suivi d'une pr�sentation de la m�thode du Simplexe. On d�crit ensuite l'algorithme de Khachiyan sans �luder les probl�mes num�riques. Viennent alors une suite d'algorithmes polynomiaux pour Optimiser � partir de l'oracle S�parer. Apr�s quelques transformations, on montre que, par polarit�, on peut S�parer � partir de l'oracle Optimiser. La premi�re �quivalence est revue apr�s avoir d�crit l'algorithme LLL. L'ouvrage se termine par la r�duction de S�parer � Appartenir.

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