TU CE GSC CE People at the Graduate School CE Principal Investigators Stefan Ulbrich - Nonlinear Optimization and Optimal Control

The research areas of the group are the development, analysis and application of novel numerical methods for finite dimensional nonlinear optimization, the analysis and numerical solution of PDE-constrained optimization problems with control or state constraints, as well as the theory and numerical approximation of optimal control problems for PDEs, in particular for flow control problems. In the context of PDE-constrained optimization, the group has contributed to various aspects that are essential for the efficient solution of complex real-world problems. It has worked on the design and analysis of efficient methods for problems with control and/or state constraints, in particular by using affine scaling and primal-dual interior point techniques. Global as well as superlinear local convergence results were obtained in a unified framework, encompassing the optimal control of elliptic PDEs, parabolic PDEs and the incompressible Navier-Stokes equations. The application of iterative solvers with multigrid-preconditioners has been studied. Adaptive inexactness-controlling multilevel optimization methods with modular interfaces to existing PDE-solvers have been developed, which control adaptive mesh refinement by error estimators and adjust the accuracy of iterative solvers inside of optimization algorithms. Particular expertise is available in the application of these algorithms to flow optimization problems. Work has been done on time-dependent optimal control problems, e.g., for discontinuous solutions of conservation laws and the compressible Navier-Stokes equations. Moreover, there is experience with shape optimization in the context of flow control and mechanical structures. In finite dimensional optimization there is interest in novel non-monotone filter-type globalization techniques and in matrix-free methods designed for large scale optimization. Algorithmic techniques from finite dimensional large scale optimization could be extended in a rigorous way to discretized infinite dimensional optimization problems.

Technische Universität Darmstadt

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