Inverse coefficient problems for variational inequalities: Optimality conditions and numerical realization

We consider the identification of a distributed parameter in an elliptic va riational inequality. On the basis of an optimal control problem formulatio n, the application of a primal-dual penalization technique enables us to pr ove the existence of multipliers giving a first order characterization of t he optimal solution. Concerning the parameter we consider different regular ity requirements. For the numerical realization we utilize a complementarit y function, which allows us to rewrite the optimality conditions as a set o f equalities. Finally, numerical results obtained from a least squares type algorithm emphasize the feasibility of our approach.