  We investigate optimality conditions for optimization problems constrained by
a class of variational inequalities of the second kind. Based on a nonsmooth
primal-dual reformulation of the governing inequality, the differentiability of
the solution map is studied. Directional differentiability is proved both for
finite-dimensional and function space problems, under suitable assumptions on
the active set. A characterization of B- and strong stationary optimal
solutions is obtained thereafter. Finally, based on the obtained first-order
information, a trust-region algorithm is proposed for the solution of the
optimization problems.
