On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints

Issue		ESAIM: COCV Volume 15, Number 2, April-June 2009


Page(s)		426 - 453
DOI		10.1051/cocv:2008038
Published online		24 June 2008

ESAIM: COCV 15 (2009) 426-453
DOI: 10.1051/cocv:2008038

On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints

Ira Neitzel and Fredi Tröltzsch

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

Received January 10, 2007. Revised July 31, 2007 and October 23, 2007. Published online June 24, 2008.

Abstract
In this paper we study Lavrentiev-type regularization concepts for linear-quadratic parabolic control problems with pointwise state constraints. In the first part, we apply classical Lavrentiev regularization to a problem with distributed control, whereas in the second part, a Lavrentiev-type regularization method based on the adjoint operator is applied to boundary control problems with state constraints in the whole domain. The analysis for both classes of control problems is investigated and numerical tests are conducted. Moreover the method is compared with other numerical techniques.

Mathematics Subject Classification. 49K20, 49N10, 49M05

Key words: Optimal control, parabolic equation, pointwise state constraints, boundary control, Lavrentiev-type regularization

© EDP Sciences, SMAI 2008

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