Simon Gottschalk, Fraunhofer ITWM

Title:
The One-shot method for optimization problems with underlying PDEs

Abstract:

Optimization problems with underlying PDEs appear in disciplines like geophysics, medical imaging, atmospheric science and aerodynamic shape design. Conventional approaches -known from the nonlinear optimization theory- are in general extremly costly. This talk introduces the One-shot method in order to solve such optimization problems with less expense. The main idea of this approach is presented in the case of a steady PDE as a constraint. It is explained how the Karush-Kuhn-Tucker conditions can be used to find an iterative method which is able to solve this problem. In the second part optimization problems with underlying unsteady PDEs are considered. It is shown how one can transform this problem into a new form such that the One-shot method is applicable.