Geodesic
On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints
ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 2, pp. 426-453

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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.

DOI : 10.1051/cocv:2008038
Classification : 49K20, 49N10, 49M05
Keywords: optimal control, parabolic equation, pointwise state constraints, boundary control, Lavrentiev-type regularization 
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     author = {Neitzel, Ira and Tr\"oltzsch, Fredi},
     title = {On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {426--453},
     publisher = {EDP-Sciences},
     volume = {15},
     number = {2},
     year = {2009},
     doi = {10.1051/cocv:2008038},
     mrnumber = {2513093},
     zbl = {1171.49017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008038/}
}
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Neitzel, Ira; Tröltzsch, Fredi. On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints. ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 2, pp. 426-453. doi: 10.1051/cocv:2008038

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