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Semi–Smooth Newton Methods for Variational Inequalities of the First Kind

Published online by Cambridge University Press:  15 March 2003

Kazufumi Ito  and
Karl Kunisch
Kazufumi Ito
Affiliation:
Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University, USA.
Karl Kunisch
Affiliation:
Institut für Mathematik, Universität Graz, Graz, Austria. karl.kunisch@uni-graz.at.
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Abstract

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.

Keywords

Semi-smooth Newton methodscontact problemsvariational inequalitiesbilateral constraintssuperlinear convergence.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 1 , January 2003 , pp. 41 - 62
Copyright
© EDP Sciences, SMAI, 2003

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