Stability of the Iteration Method for non Expansive Mappings

Lemaire, B.. "Stability of the Iteration Method for non Expansive Mappings." Serdica Mathematical Journal 22.3 (1996): 331-340. <http://eudml.org/doc/11640>.

@article{Lemaire1996,
abstract = {The general iteration method for nonexpansive mappings on a Banach space is considered. Under some assumption of fast enough convergence on the sequence of (“almost” nonexpansive) perturbed iteration mappings, if the basic method is τ−convergent for a suitable topology τ weaker than the norm topology, then the perturbed method is also τ−convergent. Application is presented to the gradient-prox method for monotone inclusions in Hilbert spaces.},
author = {Lemaire, B.},
journal = {Serdica Mathematical Journal},
keywords = {Convex Minimization; Convergence; Iteration Method; Gradient Method; Monotone Inclusions; Prox Method; Stability; iteration method; nonexpansive mappings; Banach space; convergence; gradient-prox method; monotone inclusions; Hilbert spaces},
language = {eng},
number = {3},
pages = {331-340},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Stability of the Iteration Method for non Expansive Mappings},
url = {http://eudml.org/doc/11640},
volume = {22},
year = {1996},
}

TY - JOUR
AU - Lemaire, B.
TI - Stability of the Iteration Method for non Expansive Mappings
JO - Serdica Mathematical Journal
PY - 1996
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 22
IS - 3
SP - 331
EP - 340
AB - The general iteration method for nonexpansive mappings on a Banach space is considered. Under some assumption of fast enough convergence on the sequence of (“almost” nonexpansive) perturbed iteration mappings, if the basic method is τ−convergent for a suitable topology τ weaker than the norm topology, then the perturbed method is also τ−convergent. Application is presented to the gradient-prox method for monotone inclusions in Hilbert spaces.
LA - eng
KW - Convex Minimization; Convergence; Iteration Method; Gradient Method; Monotone Inclusions; Prox Method; Stability; iteration method; nonexpansive mappings; Banach space; convergence; gradient-prox method; monotone inclusions; Hilbert spaces
UR - http://eudml.org/doc/11640
ER -