IJPAM: Volume 5, No. 3 (2003)

AN APPROXIMATE INERTIAL PROXIMAL METHOD
USING THE ENLARGEMENT OF A MAXIMAL
MONOTONE OPERATOR

A. Moudafi$^1$, E. Elisabeth
Scientific Department
University of the French West Indies and Guiana
B.P. 7209, 97275 Schoelcher Cedex, Martinique, FRANCE
and
Université des Antilles et de la Guyane
Département Scientifique Interfacultaires
B.P. 7209, 97275 Schoelcher Cedex, Martinique, F.W.I.
$^1$e-mail: abdellatif.moudafi@martinique.univ-ag.fr


Abstract.An approximate procedure for solving the problem of finding a zero of a maximal monotone operator is proposed and its convergence is established under various conditions. More precisely, it is shown that this method weakly converges under natural assumptions and strongly converges provided that either the inverse of the involved operator is Lipschitz continuous around zero or the interior of the solution set is nonempty. A particular attention is given to the convex minimization case.

Received: January 31, 2003

AMS Subject Classification: 90C25; 49M45, 65C25

Key Words and Phrases: monotone operators, elargements, proximal point algorithm, local Lipschitz continuity, approximate subdifferential, convergence, convex minimization

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 5
Issue: 3