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

Published online by Cambridge University Press:  02 July 2009

Michael Hintermüller  and
Irwin Yousept
Michael Hintermüller
Affiliation:
Department of Mathematics Humboldt-University of Berlin, Unter den Linden 6, 10099 Berlin, Germany. hint@math.hu-berlin.de Institute of Mathematics and Scientific Computing, University of Graz, 8010 Graz, Austria.
Irwin Yousept
Affiliation:
Institut für Mathematik, Technische Universität Berlin, Str. des 17. Juni 136, 10623 Berlin, Germany. yousept@math.tu-berlin.de
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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.

Keywords

Extrapolationmixed control-state constraintsPDE-constrained optimizationsemismooth Newton algorithmsensitivitystate constraints
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 16 , Issue 3 , July 2010 , pp. 503 - 522
Copyright
© EDP Sciences, SMAI, 2009

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