Error estimates for joint Tikhonov and Lavrentiev regularization of constrained control problems

Abstract

We consider joint Tikhonov and Lavrentiev regularization of control problems with pointwise control- and state-constraints. We derive error estimates for the error which is introduced by the Tikhonov regularization. With the help of these results we show that, if the solution of the unconstrained problem has no active constraints, the same holds for the Tikhonov regularized solution if the regularization parameter is small enough and a certain source condition is fulfilled.

Keywords:

• Tikhonov regularization
• Lavrentiev regularization
• pointwise inequality constraints
• optimal control
• inverse problems

AMS Subject Classifications::

• 49K20
• 49K40
• 49N45

Acknowledgements

We would like to thank Gerd and Daniel Wachsmuth for interesting discussions and helpful comments which improved the results in this article.