Geodesic
Parabolic control problems in space-time measure spaces
Casas, Eduardo1  ; Kunisch, Karl2, 3 
1 Departmento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria, 39005 Santander, Spain
2 Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010 Graz, Austria
3 Radon Institute, Austrian Academy of Sciences, 69 Alterberger Straβe, 4040 Linz, Austria
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 2, pp. 355-370

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Optimal control problems in measure spaces governed by parabolic equations with are considered. The controls appear as spatial measure in the initial condition and as space-time measures as forcing functions. First order optimality conditions are derived and certain structural properties, in particular sparsity, are discussed. An framework for approximation if these highly irregular problems is also proposed.

DOI : 10.1051/cocv/2015008
Classification : 90C48, 49J52, 49K20
Keywords: Space-time measure controls, optimal control, sparsity, parabolic equations, first order optimality conditions, numerical approximation

Casas, Eduardo 1 ; Kunisch, Karl 2, 3

1 Departmento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria, 39005 Santander, Spain
2 Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010 Graz, Austria
3 Radon Institute, Austrian Academy of Sciences, 69 Alterberger Straβe, 4040 Linz, Austria 
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     title = {Parabolic control problems in space-time measure spaces},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {355--370},
     publisher = {EDP-Sciences},
     volume = {22},
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Casas, Eduardo; Kunisch, Karl. Parabolic control problems in space-time measure spaces. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 2, pp. 355-370. doi: 10.1051/cocv/2015008

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