  We propose a nonsmooth trust-region method for solving optimization problems
with locally Lipschitz continuous functions, with application to problems
constrained by variational inequalities of the second kind. Under suitable
assumptions on the model functions, convergence of the general algorithm to a
C-stationary point is verified. For variational inequality constrained
problems, we are able to properly characterize the Bouligand subdifferential of
the reduced cost function and, based on that, we propose a computable
trust-region model which fulfills the convergence hypotheses of the general
algorithm. The article concludes with the experimental study of the main
properties of the proposed method based on two different numerical instances.
