We consider the identification of a distributed parameter in an elliptic
variational inequality. On the basis of an optimal control problem
formulation, the application of a primal-dual penalization
technique enables us to prove the existence
of multipliers giving a first order characterization of the optimal solution.
Concerning the parameter we consider different
regularity requirements. For the numerical realization we utilize a complementarity function,
which allows us to rewrite the optimality conditions as a set of equalities.
Finally, numerical results obtained from a least squares type algorithm
emphasize the feasibility of our approach.