Document ESAIM: COCV
DOI: 10.1051/cocv:2008038
On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints
Ira Neitzel and Fredi TröltzschTechnische 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