Semi-smooth Newton methods are analyzed for a class of variational inequalities in infinite dimensions. It is shown that they are equivalent to certain active set strategies. Global and local super-linear convergence are proved. To overcome the phenomenon of finite speed of propagation of discretized problems a penalty version is used as the basis for a continuation procedure to speed up convergence. The choice of the penalty parameter can be made on the basis of an
Mots-clés : semi-smooth Newton methods, contact problems, variational inequalities, bilateral constraints, superlinear convergence
@article{M2AN_2003__37_1_41_0,
author = {Ito, Kazufumi and Kunisch, Karl},
title = {Semi-smooth {Newton} methods for variational inequalities of the first kind},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {41--62},
publisher = {EDP-Sciences},
volume = {37},
number = {1},
year = {2003},
doi = {10.1051/m2an:2003021},
zbl = {1027.49007},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an:2003021/}
}
TY - JOUR AU - Ito, Kazufumi AU - Kunisch, Karl TI - Semi-smooth Newton methods for variational inequalities of the first kind JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2003 SP - 41 EP - 62 VL - 37 IS - 1 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an:2003021/ DO - 10.1051/m2an:2003021 LA - en ID - M2AN_2003__37_1_41_0 ER -
%0 Journal Article %A Ito, Kazufumi %A Kunisch, Karl %T Semi-smooth Newton methods for variational inequalities of the first kind %J ESAIM: Modélisation mathématique et analyse numérique %D 2003 %P 41-62 %V 37 %N 1 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an:2003021/ %R 10.1051/m2an:2003021 %G en %F M2AN_2003__37_1_41_0
Ito, Kazufumi; Kunisch, Karl. Semi-smooth Newton methods for variational inequalities of the first kind. ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 1, pp. 41-62. doi : 10.1051/m2an:2003021. https://www.numdam.org/articles/10.1051/m2an:2003021/
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