"2003 Colloquium on Differential Equations and Applications, Maracaibo, Venezuela. Electronic Journal of Differential Equations, Conference 13, 2005, pp. 13-19. Title: Method of relaxation applied to optimization of discrete systems Authors: Jean Louis Calvet (Laboratoire d'Analyse, Toulouse, France) Juan Cardillo (Univ. de Los Andes, Merida, Venezuela) Jean Claude Hennet (Laboratoire d'Analyse, Toulouse, France) Ferenc Szigeti (Univ. de Los Andes, Merida, Venezuela) Abstract: In this work, the relaxation method is presented and then applied to the optimization of a family of discrete systems. Thus, a condition for the relationship between the minimum of the original problem and of the relaxed problem is translated to an equivalent condition of minimum principle. Several examples illustrate this technique and the condition obtained. Published May 30, 2005. Math Subject Classifications: 93C65, 49M20, 74P20 Key Words: Discrete Systems; relaxation; optimization