  In this paper we present GSSN, a globalized SCD semismooth* Newton method for
solving nonsmooth nonconvex optimization problems. The global convergence
properties of the method are ensured by the proximal gradient method, whereas
locally superlinear convergence is established via the SCD semismooth* Newton
method under quite weak assumptions. The Newton direction is based on the SC
(subspace containing) derivative of the subdifferential mapping and can be
computed by the (approximate) solution of an equality-constrained quadratic
program. Special attention is given to the efficient numerical implementation
of the overall method.
