Convergence variationnelle et opérateurs maximaux monotones d'un espace de Hilbert réel

Following an idea due to H. Attouch and R.J.B. Wets in the context of variational convergence theory and convex optimization, we introduce, on the set of maximal monotone operators on a real Hilbert space, a parametric semi-distance, which induces a stronger notion of convergence than the graph convergence. This metric is fundamental in the theoretical study of algorithms for searching a zero of a maximal monotone operator on a real Hilbert space.