TY - GEN A1 - Schiela, Anton T1 - A continuity result for Nemyckii Operators and some applications in PDE constrained optimal control N2 - This work explores two applications of a classical result on the continuity of Nemyckii operators to optimal control with PDEs. First, we present an alternative approach to the analysis of Newton's method for function space problems involving semi-smooth Nemyckii operators. A concise proof for superlinear convergence is presented, and sharpened bounds on the rate of convergence are derived. Second, we derive second order sufficient conditions for problems, where the underlying PDE has poor regularity properties. We point out that the analytical structure in both topics is essentially the same. T3 - ZIB-Report - 06-41 KW - continuity of Nemyckii Operators KW - Newton methods in function space KW - optimal control KW - second order sufficient conditions Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9354 ER - TY - GEN A1 - Schiela, Anton T1 - Convergence of the Control Reduced Interior Point Method for PDE Constrained Optimal Control with State Constraints N2 - We propose a variant of the control reduced interior point method for the solution of state constrained problems. We show convergence of the corresponding interior point pathfollowing algorithm in function space. Morever, we provide error bounds for the iterates. T3 - ZIB-Report - 06-16 KW - interior point methods in function space KW - optimal control KW - state constraints Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9099 ER - TY - GEN A1 - Schiela, Anton A1 - Weiser, Martin T1 - Superlinear Convergence of the Control Reduced Interior Point Method for PDE Constrained Optimization N2 - A thorough convergence analysis of the Control Reduced Interior Point Method in function space is performed. This recently proposed method is a primal interior point pathfollowing scheme with the special feature, that the control variable is eliminated from the optimality system. Apart from global linear convergence we show, that this method converges locally almost quadratically, if the optimal solution satisfies a function space analogue to a non-degeneracy condition. In numerical experiments we observe, that a prototype implementation of our method behaves in compliance with our theoretical results. T3 - ZIB-Report - 05-15 KW - interior point methods in function space KW - optimal control KW - superlinear convergence Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8490 ER -