Prof. Stefan Ulbrich, Nonlinear Optimization, TU Darmstadt

Title:
Robust Nonconvex PDE-Constrained Optimization based on Second Order Approximation Techniques and Reduced Order Models

Abstract:

We consider robust optimization techniques for nonconvex PDE-constrained problems involving uncertain parameters. The parameters are assumed to be contained in a given uncertainty set. This type of robust optimization problems are difficult to treat computationally and hence suitable approximations and solution methods are required. We propose and investigate an approximate robust formulation that employs a quadratic approximation (or only a linear approximation when appropriate) and can be solved efficiently by using a full-space formulation as mathematical program with equilibrium constraints (MPEC) or a reduced formulation. Moreover, we consider the application of reduced order models with a posteriori error estimation within the optimization method to reduce the number of required PDE-solves during the optimization.
We show applications to the robust geometry optimization of a permanent magnet synchronous motor and to the robust geometry optimization of load-carrying structures governed by the elastodynamic equations.

This is joint work with Oliver Lass and Philip Kolvenbach, TU Darmstadt.