Solving variational inclusions by a multipoint iteration method under center-Hölder continuity conditions

Catherine Cabuzel, and Alain Pietrus. "Solving variational inclusions by a multipoint iteration method under center-Hölder continuity conditions." Applicationes Mathematicae 34.4 (2007): 493-503. <http://eudml.org/doc/280036>.

@article{CatherineCabuzel2007,
abstract = {We prove the existence of a sequence $(x_k)$ satisfying $0 ∈ f(x_k) +∑_\{i=1\}^M a_i ∇ f(x_k+β_i(x_\{k+1\}-x_k))(x_\{k+1\}-x_k)+F(x_\{k+1\})$, where f is a function whose second order Fréchet derivative ∇²f satifies a center-Hölder condition and F is a set-valued map from a Banach space X to the subsets of a Banach space Y. We show that the convergence of this method is superquadratic.},
author = {Catherine Cabuzel, Alain Pietrus},
journal = {Applicationes Mathematicae},
keywords = {set-valued mapping; generalized equations; Aubin continuity; pseudo-Lipschitz map; multipoint iteration formula; center-Hölder continuity},
language = {eng},
number = {4},
pages = {493-503},
title = {Solving variational inclusions by a multipoint iteration method under center-Hölder continuity conditions},
url = {http://eudml.org/doc/280036},
volume = {34},
year = {2007},
}

TY - JOUR
AU - Catherine Cabuzel
AU - Alain Pietrus
TI - Solving variational inclusions by a multipoint iteration method under center-Hölder continuity conditions
JO - Applicationes Mathematicae
PY - 2007
VL - 34
IS - 4
SP - 493
EP - 503
AB - We prove the existence of a sequence $(x_k)$ satisfying $0 ∈ f(x_k) +∑_{i=1}^M a_i ∇ f(x_k+β_i(x_{k+1}-x_k))(x_{k+1}-x_k)+F(x_{k+1})$, where f is a function whose second order Fréchet derivative ∇²f satifies a center-Hölder condition and F is a set-valued map from a Banach space X to the subsets of a Banach space Y. We show that the convergence of this method is superquadratic.
LA - eng
KW - set-valued mapping; generalized equations; Aubin continuity; pseudo-Lipschitz map; multipoint iteration formula; center-Hölder continuity
UR - http://eudml.org/doc/280036
ER -