Proximal Penalty Method for Ill-Posed Parabolic Optimal Control Problems
Alexander Kaplan, Rainer Tichatschke · Birkhäuser Basel eBooks · 1998
The application of a proximal point approach to ill-posed 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.