  In this paper we present an abstract nonsmooth optimization problem for which
we recall existence and uniqueness results. We show a numerical scheme to
approximate its solution. The theory is later applied to a sample static
contact problem describing an elastic body in frictional contact with a
foundation. This problem leads to a hemivariational inequality which we solve
numerically. Finally, we compare three computational methods of solving contact
mechanical problems: direct optimization method, augmented Lagrangian method
and primal-dual active set strategy.
