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A new stopping criterion for iterative solvers for control optimal problems

Krumbiegel K., Rosch A.

Archives of Control Sciences

2008

Vol. 18, no. 1

17-42

Linear quadratic optimal control problems governed by PDEs with pointwise control constraints are considered. We derive error estimates for feasible and infeasible controls of the problem. Based on this theory an error estimator is constructed for different discretization schemes. Moreo ver, we establish the estimator as a stopping criterion for several optimization methods. Furthermore, additional errors caused by solving the linear systems are discussed. The theory is illustrated by numerical examples.

Regularized penalty method for non-coercive parabolic optimal control problems

Kaplan A., Tichatschke R.

Control and Cybernetics

1998

Vol. 27, no 1

5-27

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.