Publication ahead of print Issue ESAIM: COCV DOI 10.1051/cocv/2009016 Published online 02 July 2009

ESAIM: COCV
DOI: 10.1051/cocv/2009016

A sensitivity-based extrapolation technique for the numerical solution of state-constrained optimal control problems

Michael Hintermüller^{1, 2} and Irwin Yousept<sup>3

1</sup>  Department of Mathematics Humboldt-University of Berlin, Unter den Linden 6, 10099 Berlin, Germany. hint@math.hu-berlin.de
²  Institute of Mathematics and Scientific Computing, University of Graz, 8010 Graz, Austria.
³  Institut für Mathematik, Technische Universität Berlin, Str. des 17. Juni 136, 10623 Berlin, Germany. yousept@math.tu-berlin.de

Received July 13, 2007. Revised January 28, 2009. Published online July 2nd, 2009.

Abstract
Sensitivity analysis (with respect to the regularization parameter) of the solution of a class of regularized state constrained optimal control problems is performed. The theoretical results are then used to establish an extrapolation-based numerical scheme for solving the regularized problem for vanishing regularization parameter. In this context, the extrapolation technique provides excellent initializations along the sequence of reducing regularization parameters. Finally, the favorable numerical behavior of the new method is demonstrated and a comparison to classical continuation methods is provided.

Mathematics Subject Classification. 49M15, 49M37, 65K05, 90C33

Key words: Extrapolation, mixed control-state constraints, PDE-constrained optimization, semismooth Newton algorithm, sensitivity, state constraints


© EDP Sciences, SMAI 2009

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