On convergence of Lavrentiev regularization for semilinear parabolic optimal control problems with pointwise control and state constraints

We consider Lavrentiev regularization for a class of semilinear parabolic optimal control problems with control constraints and pointwise state constraints and review convergence results for local solutions under Slater type assumptions as well as quadratic growth conditions. Moreover, we state a local uniqueness result for local optima under the assumptions of strict separability of the active sets as well as a second order sufficient condition for the regularized solution. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)