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The paper starts with a concise description of the recently developedsemismooth* Newton method for the solution of general inclusions. This methodis then applied to a class of variational inequalities of the second kind. As aresult, one obtains an implementable algorithm exhibiting a local superlinearconvergence. Thereafter we suggest several globally convergent hybridalgorithms in which one combines the semismooth* Newton method with selectedsplitting algorithms for the solution of monotone variational inequalities.Their efficiency is documented by extensive numerical experiments.

On the application of the semismooth* Newton method to variational inequalities of the second kind