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 areproved. To overcome the phenomenon of finite speed of propagation of discretized problems a penalty versionis 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.
