SUFFICIENT OPTIMALITY CONDITIONS FOR THE MOREAU-YOSIDA TYPE REGULARIZATION CONCEPT APPLIED TO SEMILINEAR ELLIPTIC OPTIMAL CONTROL PROBLEMS WITH POINTWISE STATE CONSTRAINTS

We develop sufficient optimality conditions for a Moreau-Yosidaregularized optimal control problem governed by a semilinear ellipticPDE with pointwise constraints on the state and the control. We makeuse of the equivalence of a setting of Moreau-Yosida regularization to a special setting of the virtual control concept,for which standard second order sufficient conditions have been shown. Moreover, we present a numerical example,solving a Moreau-Yosida regularized model problem with an SQP method.