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. KW - continuity of Nemyckii Operators KW - Newton methods in function space KW - optimal control Y1 - 2008 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/498 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-4984 ER -