Semi–Smooth Newton Methods for Variational Inequalities of the First Kind
Center for Research in Scientific Computation, Department of Mathematics,
North Carolina State University, USA.
2 Institut für Mathematik, Universität Graz, Graz, Austria. email@example.com.
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