@misc{PruefertTroeltzschWeiser, author = {Pr{\"u}fert, Uwe and Tr{\"o}ltzsch, Fredi and Weiser, Martin}, title = {The convergence of an interior point method for an elliptic control problem with mixed control-state constraints}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8223}, number = {04-47}, abstract = {The paper addresses primal interior point method for state constrained PDE optimal control problems. By a Lavrentiev regularization, the state constraint is transformed to a mixed control-state constraint with bounded Lagrange multiplier. Existence and convergence of the central path are established, and linear convergence of a short-step pathfollowing method is shown. The behaviour of the regularizations are demonstrated by numerical examples.}, language = {en} } @article{PruefertTroeltzschWeiser2008, author = {Pr{\"u}fert, Uwe and Tr{\"o}ltzsch, Fredi and Weiser, Martin}, title = {The convergence of an interior point method for an elliptic control problem with mixed control-state constraints}, series = {Comput. Optim. Appl.}, volume = {39}, journal = {Comput. Optim. Appl.}, number = {2}, pages = {183 -- 218}, year = {2008}, language = {en} } @article{PruefertTroeltzsch2007, author = {Pr{\"u}fert, Uwe and Tr{\"o}ltzsch, Fredi}, title = {An interior point method for a parabolic optimal control problem with regularized pointwise state constraints}, series = {ZAMM}, volume = {87}, journal = {ZAMM}, number = {8-9}, address = {Berlin}, doi = {10.1002/zamm.200610337}, pages = {564 -- 589}, year = {2007}, language = {en} } @misc{PruefertSchiela, author = {Pr{\"u}fert, Uwe and Schiela, Anton}, title = {The minimization of an L^{\infty}-functional subject to an elliptic PDE and state constraints}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10714}, number = {08-17}, abstract = {We study the optimal control of a maximum-norm objective functional subject to an elliptic-type PDE and pointwise state constraints. The problem is transformed into a problem where the non-differentiable L^{\infty}-norm in the functional will be replaced by a scalar variable and additional state constraints. This problem is solved by barrier methods. We will show the existence and convergence of the central path for a class of barrier functions. Numerical experiments complete the presentation.}, language = {en} } @article{PruefertSchiela2009, author = {Pr{\"u}fert, Uwe and Schiela, Anton}, title = {The Minimization of a maximum-norm functional subject to an elliptic PDE and state constraints}, series = {Z. angew. Math. Mech.}, volume = {89}, journal = {Z. angew. Math. Mech.}, number = {7}, pages = {536 -- 551}, year = {2009}, language = {en} } @article{NeitzelPruefertSlawig2007, author = {Neitzel, Ira and Pr{\"u}fert, Uwe and Slawig, Thomas}, title = {Strategies for time-dependent PDE control using an integrated modeling and simulation environment. Part one}, number = {408}, publisher = {Matheon}, address = {Berlin}, year = {2007}, language = {en} } @article{NeitzelPruefertSlawig2007, author = {Neitzel, Ira and Pr{\"u}fert, Uwe and Slawig, Thomas}, title = {Strategies for time-dependent PDE control using an integrated modeling and simulation environment. Part two}, number = {24-02}, publisher = {SPP 1253}, year = {2007}, language = {en} } @article{MeyerPruefertTroeltzsch2007, author = {Meyer, Christian and Pr{\"u}fert, Uwe and Tr{\"o}ltzsch, Fredi}, title = {On two numerical methods for state-constrained elliptic control problems}, series = {Optimization Methods and Software}, volume = {22}, journal = {Optimization Methods and Software}, number = {6}, pages = {871 -- 899}, year = {2007}, language = {en} }