| Issue |
ESAIM: M2AN
Volume 37, Number 1, January/February 2003
|
|
|---|---|---|
| Page(s) | 41 - 62 | |
| DOI | https://doi.org/10.1051/m2an:2003021 | |
| Published online | 15 March 2003 | |
Semi–Smooth Newton Methods for Variational Inequalities of the First Kind
1
Center for Research in Scientific Computation, Department of Mathematics,
North Carolina State University, USA.
2
Institut für Mathematik, Universität Graz, Graz, Austria. karl.kunisch@uni-graz.at.
Received:
15
April
2002
Revised:
30
July
2002
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∞ estimate for the penalized solutions. Unilateral as well as bilateral problems are considered.
Mathematics Subject Classification: 49J40 / 65K10
Key words: Semi-smooth Newton methods / contact problems / variational inequalities / bilateral constraints / superlinear convergence.
© EDP Sciences, SMAI, 2003
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.