Journal of Convex Analysis 14 (2007), No. 4, 869--878
Copyright Heldermann Verlag 2007
A Proximal Method for Maximal Monotone Operators via Discretization of a First Order Dissipative Dynamical System
Paul-Emile Maingé
GRIMMAG, Université des Antilles-Guyane, Dép. Scientifique Interfacultaire, Campus de Schoelcher, 97230 Martinique, France
paul-emile.mainge@martinique.univ-ag.fr
Abdellatif Moudafi
GRIMMAG, Université des Antilles-Guyane, Dép. Scientifique Interfacultaire, Campus de Schoelcher, 97230 Martinique, France
abdellatif.moudafi@martinique.univ-ag.fr
We present an iterative method for finding zeroes of maximal monotone operators in a real Hilbert space. The underlying idea relies upon the discretization of a first order dissipative dynamical system which allows us to preserve the local feature, as well as to obtain convergence results. The main theorems do not only recover known convergence results of standard and inertial proximal methods, but also provide a theoretical basis for the application of new iterative methods.
Keywords: Monotone operators, standard and inertial proximal methods, minimization.
MSC: 49J53, 65K10; 49M37, 90C25
[ Fulltext-pdf (108 KB)] for subscribers only.