"Optimization problems with time-periodic PDE constraints"
Andreas Potschka Interdisciplinary Center for Scientific Computing (IWR)Heidelberg University
Optimization problems with time-periodic parabolic PDE constraints arise in important application areas, e.g., in chemical engineering. The resulting nonlinear dynamical optimization problems are difficult, especially because they feature free initial values. We present a novel direct numerical optimization method based on inexact Sequential Quadratic Programming (SQP) with a two-grid Newton-Picard preconditioned Linear Iterative Splitting Approach (LISA) for the quadratic subproblems (QPs). The method features fast linear convergence that is independent of the degrees of freedom for the fine spatial discretization grid. We demonstrate how the arising large-scale QPs can be solved efficiently via intelligent structure exploitation. Moreover, we address issues of affine-invariant globalization of convergence and discuss local convergence of LISA-SQP in the framework of Bock's kappa-Theory. We present how novel a-posteriori kappa-estimators can be used to control the local rate of convergence by adaptively choosing the coarse grid from a given hierarchy of grid levels. Finally, we illustrate the performance of the method by numerical results for three application problems ranging from an academic model problem to a real-world periodic adsorption process.
Two OPTEC professors have been awarded three "Gouden Krijtjes", the yearly teaching awards given by the organization of engineering students (vtk). Prof. Lombaert was awarded the prize for the best course in civil engineering, and Prof. Diehl the prizes for the best professor and the best course in mathematical engineering (where he teaches numerical optimization). They received these awards at the yearly "proffentap" where experienced students taught them how to draft beer professionally.
