  In this paper, we investigate optimal control problems governed by semilinear
elliptic variational inequalities involving constraints on the state, and more
precisely the obstacle problem. Since we adopt a numerical point of view, we
first relax the feasible domain of the problem, then using both mathematical
programming methods and penalization methods we get optimality conditions with
smooth Lagrange multipliers. Some numerical experiments using IPOPT algorithm
are presented to verify the efficiency of our approach.
