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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 pointwise bilateral control-state constraints are considered. A locally superlinearly convergent numerical solution algorithm is proposed and its mesh independence is established. Further, for the efficient numerical solution reduced space and Schur complement based preconditioners are proposed which take into account the active and inactive set structure of the problem. The paper ends by numerical tests illustrating our theoretical findings and comparing the efficiency of the proposed preconditioners.

Keywords

Bilateral control-state constraintsheat equationmesh independenceoptimal controlPDE-constrained optimizationsemismooth Newton method
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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