18th GAMM-Seminar Leipzig on
Multigrid and related methods for optimization problems

Max-Planck-Institute for Mathematics in the Sciences
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  18th GAMM-Seminar
January, 24th-26th, 2002
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  Abstract Martin Weiser, Fri, 11.45-12.25 Previous Contents Next  
  An Adaptive Function Space Interior Point Method for Optimal Control Problems
Martin Weiser (Konrad-Zuse-Zentrum für Informationstechnik Berlin)

A new approach to the numerical solution of optimal control problems including control and state constraints is presented. Like hybrid methods, the approach aims at combining the advantages of direct and indirect methods. Unlike hybrid methods, however, our method is directly based on {\em interior-point concepts in function space} -- realized via an {\em adaptive multilevel scheme} applied to the complementarity formulation and to numerical continuation along the central path. Existence of the central path and its continuation towards the solution point is briefly analyzed. An adaptive stepsize control with respect to the duality gap parameter is worked out in more detail in the framework of affine invariant inexact Newton methods. Finally, the performance of a prototype of our algorithm is documented by the successful treatment of the well-known intricate {\em windshear problem} treated by Bulirsch et al.

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Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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