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Mesh-independence and preconditioning for solving parabolic control problems with mixed control-state constraints

Published online by Cambridge University Press:  19 July 2008

Michael Hintermüller ,
Ian Kopacka  and
Stefan Volkwein
Michael Hintermüller
Affiliation:
University of Sussex Department of Mathematics Mantell Building Falmer, Brighton BN1 9RF, UK. michael.hintermueller@uni-graz.at
Ian Kopacka
Affiliation:
Karl-Franzens-University of Graz Department of Mathematics and Scientific Computing Heinrichstrasse 36, 8010 Graz, Austria. ian.kopacka@uni-graz.at; stefan.volkwein@uni-graz.at
Stefan Volkwein
Affiliation:
Karl-Franzens-University of Graz Department of Mathematics and Scientific Computing Heinrichstrasse 36, 8010 Graz, Austria. ian.kopacka@uni-graz.at; stefan.volkwein@uni-graz.at
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Abstract

Optimal control problems for the heat equation with pointwisebilateral control-state constraints are considered. A locallysuperlinearly convergent numerical solution algorithm is proposedand its mesh independence is established. Further, for theefficient numerical solution reduced space and Schur complementbased preconditioners are proposed which take into account theactive and inactive set structure of the problem. The paper endsby numerical tests illustrating our theoretical findings andcomparing the efficiency of the proposed preconditioners.

Keywords

Bilateral control-state constraintsheat equationmeshindependenceoptimal controlPDE-constrained optimizationsemismooth Newton method

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 15 , Issue 3 , July 2009 , pp. 626 - 652
Copyright
© EDP Sciences, SMAI, 2008

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