Semi-smooth Newton methods for variational inequalities of the first kind
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 37 (2003) no. 1, p. 41-62

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 ${L}^{\infty }$ estimate for the penalized solutions. Unilateral as well as bilateral problems are considered.

DOI : https://doi.org/10.1051/m2an:2003021
Classification:  49J40,  65K10
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {37},
number = {1},
year = {2003},
pages = {41-62},
doi = {10.1051/m2an:2003021},
zbl = {1027.49007},
language = {en},
url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Volume 37 (2003) no. 1, pp. 41-62. doi : 10.1051/m2an:2003021. http://www.numdam.org/item/M2AN_2003__37_1_41_0/

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