  In this paper we introduce an abstract nonsmooth optimization problem and
prove existence and uniqueness of its solution. We present a numerical scheme
to approximate this solution. The theory is later applied to a sample static
contact problem describing an elastic body in frictional contact with a
foundation. This contact is governed by a nonmonotone friction law with
dependence on normal and tangential components of displacement. Finally,
computational simulations are performed to illustrate obtained results.
