  The paper starts with a description of the SCD (subspace containing
derivative) mappings and the SCD semismooth* Newton method for the solution of
general inclusions. This method is then applied to a class of variational
inequalities of the second kind. As a result, one obtains an implementable
algorithm exhibiting a locally superlinear convergence. Thereafter we suggest
several globally convergent hybrid algorithms in which one combines the SCD
semismooth* Newton method with selected splitting algorithms for the solution
of monotone variational inequalities. Finally we demonstrate the efficiency of
one of these methods via a Cournot-Nash equilibrium, modeled as a variational
inequalities of the second kind, where one admits really large numbers of
players (firms) and produced commodities.
