Oberseminar Numerische Mathematik / Scientific Computing
Forschen im Foyer
Michael Hintermüller
HU-Berlin
Optimal control and design subject to variational inequalities
Abstract:
Many applications, such as the optimization of packaging problems or contact problems, parameter identification in engineering applications (lubrication) or mathematical finance (American put options) or optimizing the shape in electrochemical machining, lead to minimization tasks where one of the constraints is a variational inequality. The resulting optimizati- on problems are challenging as classical constraint qualifications for deriving ”Lagrange” multipliers generically fail. Hence, besides the development of a stable numerical solution scheme for the underlying problem class, already the development of suitable first order optimality conditions is an issue. In this talk several constructive analytic approaches for deriving stationarity conditions for optimization problems with variational inequality constraints are discussed. It is demonstrated that depending on the utilized technique different stationarity principles may be reached. ’Constructive’ refers here to the fact that the respective proof technique can be cast into a numerical scheme relying on semismooth Newton techniques and/or nonlinear multigrid methods. In the context of shape optimization sub ject to variational inequa- lities, shape and topological sensitivity analysis is performed. The resulting shape and topological gradients (or rather directional derivatives) are then used within gradient or Newton-type descent algorithms. The talk ends by a report on numerical tests and an outlook on future directions in the field.
| Datum: | 08.06.09 | Zeit: | 17:00 Uhr | Ort: | FU Berlin, Institut für Mathematik, Arnimallee 6, 14195 Berlin. | Raum: | Foyer im Erdgeschoss |