We consider control constrained and state constrained optimal control problems governed by elliptic partial differential equations, once they have been discretized. We propose and analyze an algorithm for efficient solution of these finite dimensional problems. It is based on an active set strategy involving primal as well as dual variables and is suggested by a generalized Moreau-Yosida regularization of the control (or state) constraint. Sufficient conditions for convergence in finitely many iterations are given. At last we present numerical examples and discuss the role of the strict complementarity condition.