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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 estimate for the penalized solutions. Unilateral as well as bilateral problems are considered.
@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: Mathematical Modelling and Numerical Analysis },
pages = {41--62},
publisher = {EDP-Sciences},
volume = {37},
number = {1},
year = {2003},
doi = {10.1051/m2an:2003021},
zbl = {1027.49007},
language = {en},
url = {http://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis PY - 2003 SP - 41 EP - 62 VL - 37 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis %D 2003 %P 41-62 %V 37 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis , Tome 37 (2003) no. 1, pp. 41-62. doi : 10.1051/m2an:2003021. http://geodesic.mathdoc.fr/articles/10.1051/m2an:2003021/
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