We consider the identification of a distributed parameter in an ellipticvariational inequality. On the basis of an optimal control problemformulation, the application of a primal-dual penalizationtechnique enables us to prove the existenceof multipliers giving a first order characterization of the optimal solution.Concerning the parameter we consider differentregularity 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 algorithmemphasize the feasibility of our approach.
