In this note we show that the splitting scheme of Passty [7] as well as the barycentric-proximal method of Lehdili & Lemaire [4] can be used to approximate a zero of the extended sum of maximal monotone operators. When the extended sum is maximal monotone, we extend the convergence result obtained by Lehdili & Lemaire for convex functions to the case of maximal monotone operators. Moreover, we recover the main convergence results by Passty and Lehdili & Lemaire when the pointwise sum of the involved operators is maximal monotone.
Publié le : 2000-07-05
Classification:
maximal monotone operators,
Yosida regularization,
enlargements,
variational sum,
extended sum,
splitting methods,
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
@article{hal-00783905,
author = {Moudafi, Abdellatif and Th\'era, Michel},
title = {Ergodic Convergence to a Zero of the Extended Sum},
journal = {HAL},
volume = {2000},
number = {0},
year = {2000},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00783905}
}
Moudafi, Abdellatif; Théra, Michel. Ergodic Convergence to a Zero of the Extended Sum. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-00783905/