TY - GEN A1 - Prüfert, Uwe A1 - Tröltzsch, Fredi A1 - Weiser, Martin T1 - The convergence of an interior point method for an elliptic control problem with mixed control-state constraints N2 - 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. T3 - ZIB-Report - 04-47 KW - interior point methods in function space KW - optimal control KW - mixed control-state constraints KW - Lavrentiev regularization Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8223 ER - TY - GEN A1 - Volkwein, S. A1 - Tröltzsch, Fredi T1 - POD a-posteriori error estimates for linear-quadratic optimal control problems Y1 - 2007 IS - SFB-Report 2007-008 PB - SFB Research Center "Mathematical Optimization and Applications in Biomedical Sciences", Karl-Franzens-Universität Graz ER - TY - JOUR A1 - Casas, E. A1 - de Los Reyes, J. A1 - Tröltzsch, Fredi T1 - Sufficient second-order optimality conditions for semilinear control problems with pointwise state constraints JF - SIAM Journal on Optimization Y1 - 2007 U6 - https://doi.org/10.1137/07068240X VL - 19 IS - 2 SP - 616 EP - 643 ER - TY - JOUR A1 - Meyer, Christian A1 - Prüfert, Uwe A1 - Tröltzsch, Fredi T1 - On two numerical methods for state-constrained elliptic control problems JF - Optimization Methods and Software Y1 - 2007 UR - http://www.math.tu-berlin.de/~pruefert/Publicat/index_en.html UR - /homes/numerik/pruefert/WWW/Publicat/on2numerical.pdf VL - 22 IS - 6 SP - 871 EP - 899 ER - TY - JOUR A1 - Prüfert, Uwe A1 - Tröltzsch, Fredi T1 - An interior point method for a parabolic optimal control problem with regularized pointwise state constraints JF - ZAMM Y1 - 2007 UR - http://www.math.tu-berlin.de/~pruefert/Publicat/index_en.html U6 - https://doi.org/10.1002/zamm.200610337 VL - 87 IS - 8–9 SP - 564 EP - 589 CY - Berlin ER - TY - JOUR A1 - Prüfert, Uwe A1 - Tröltzsch, Fredi A1 - Weiser, Martin T1 - The convergence of an interior point method for an elliptic control problem with mixed control-state constraints JF - Comput. Optim. Appl. Y1 - 2008 VL - 39 IS - 2 SP - 183 EP - 218 ER -