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{\large Michael Ulbrich \\
{\bf A class of regularization methods for optimal control problems with PDE and state constraints }}

Chair for Mathematical Optimization \\ Department of Mathematics \\ Technische Universitaet Muenchen \\ Boltzmannstr 3 \\ 85747 Garching \\ Germany
\\
{\tt mulbrich@ma.tum.de}\end{center}

In this talk, PDE-constrained optimal control problems with state
constraints are considered. A particular difficulty with state
constraints is that the optimality system contains complementarity
conditions between a function in a quite regular space, e.g.,
$C(\bar\Omega)$, and a generalized function in the dual space, having low
regularity, e.g., the space of Borel measures.
A general approach to tackle this situation is to introduce a suitable
family of regularized problems and to follow the path of regularized
solutions towards the solution of the state-constrained problem.
In this talk, we investigate a class of regularization methods for state
constrained optimal control problems that is related to penalty barrier
multiplier methods as well as to the Moreau-Yosida regularization.
We investigate the convergence properties of this class of methods and
develop error estimates. The presented results are also applicable to
related settings such as obstacle problems. The talk is concluded by
numerical results.


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