Semi-smooth Newton methods for optimal control problems governed by the wave equation and subject to pointwise inequality control constraints are analyzed. These methods can be equivalently reformulated as primal-dual active set strategies (PDAS). We consider diferent situations: optimal distributed control, optimal Neumann boundary control and optimal Dirichlet boundary control. In the first two situations we prove superlinear convergence of PDAS. In the last one based on the very weak solution of the wave equation we show, that there is no special smoothing property allowing to prove superlinear convergence. However, when considering the damped wave equation we can prove superlinear convergence also for the case of optimal Dirichlet boundary control. A discretization based on space-time finite elements is proposed and numerical examples are presented.
This is joint work with Karl Kunisch and Boris Vexler