Regularized penalty method for non-coercive parabolic optimal control problems

The application of a proximal point approach to illposed convex control problems governed by linear parabolic equations is studied. A stable penalty method is constructed by means of multi-step proximal regularization (only w.r.t. the control functions) in the penalized problems. For distributed control problems with state constraints convergence of the approximately determined solutions of the regularized problems to an optimal process is proved.