@misc{Schiela2007, author = {Schiela, Anton}, title = {Barrier Methods for Optimal Control Problems with State Constraints}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9504}, number = {07-07}, year = {2007}, abstract = {We study barrier methods for state constrained optimal control problems with PDEs. In the focus of our analysis is the path of minimizers of the barrier subproblems with the aim to provide a solid theoretical basis for function space oriented path-following algorithms. We establish results on existence, continuity and convergence of this path. Moreover, we consider the structure of barrier subdifferentials, which play the role of dual variables.}, language = {en} } @misc{Schiela2007, author = {Schiela, Anton}, title = {An Interior Point Method in Function Space for the Efficient Solution of State Constrained Optimal Control Problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10471}, number = {07-44}, year = {2007}, abstract = {We propose and analyse an interior point path-following method in function space for state constrained optimal control. Our emphasis is on proving convergence in function space and on constructing a practical path-following algorithm. In particular, the introduction of a pointwise damping step leads to a very efficient method, as verified by numerical experiments.}, language = {en} }