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On regularization methods for the numerical solutionof paraboliccontrol problems with pointwisestate constraints

Published online by Cambridge University Press:  24 June 2008

Ira Neitzel and
Fredi Tröltzsch
Ira Neitzel
Affiliation:
Technische Universität Berlin, Fakultät II – Mathematik und Naturwissenschaften, Str. des 17. Juni 136, 10623 Berlin, Germany. neitzel@math.tu-berlin.de; troeltz@math.tu-berlin.de
Fredi Tröltzsch
Affiliation:
Technische Universität Berlin, Fakultät II – Mathematik und Naturwissenschaften, Str. des 17. Juni 136, 10623 Berlin, Germany. neitzel@math.tu-berlin.de; troeltz@math.tu-berlin.de
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Abstract

In this paper we study Lavrentiev-type regularization concepts forlinear-quadratic parabolic control problems with pointwise state constraints. Inthe first part, we apply classical Lavrentiev regularization to a problem withdistributed control, whereas in the second part, a Lavrentiev-typeregularization method based on the adjoint operator is applied to boundarycontrol problems with state constraints in the whole domain. The analysis forboth classes of control problems is investigated and numerical tests areconducted. Moreover the method is compared with other numerical techniques.

Keywords

Optimal controlparabolic equationpointwise state constraintsboundary controlLavrentiev-typeregularization

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Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 15 , Issue 2 , April 2009, pp. 426 - 453
Copyright
© EDP Sciences, SMAI, 2008

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