@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} } @misc{VolkweinTroeltzsch2007, author = {Volkwein, S. and Tr{\"o}ltzsch, Fredi}, title = {POD a-posteriori error estimates for linear-quadratic optimal control problems}, number = {SFB-Report 2007-008}, publisher = {SFB Research Center "Mathematical Optimization and Applications in Biomedical Sciences", Karl-Franzens-Universit{\"a}t Graz}, year = {2007}, language = {en} } @article{CasasdeLosReyesTroeltzsch2007, author = {Casas, E. and de Los Reyes, J. and Tr{\"o}ltzsch, Fredi}, title = {Sufficient second-order optimality conditions for semilinear control problems with pointwise state constraints}, series = {SIAM Journal on Optimization}, volume = {19}, journal = {SIAM Journal on Optimization}, number = {2}, doi = {10.1137/07068240X}, pages = {616 -- 643}, 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} } @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} } @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} }