| Issue |
ESAIM: COCV
Volume 23, Number 1, January-March 2017
|
|
|---|---|---|
| Page(s) | 263 - 295 | |
| DOI | https://doi.org/10.1051/cocv/2015048 | |
| Published online | 09 December 2016 | |
Analysis of Spatio-Temporally Sparse Optimal Control Problems of Semilinear Parabolic Equations∗
1 Departamento de Matemática Aplicada y
Ciencias de la Computación, E.T.S.I. Industriales y de Telecomunicación, Universidad
de Cantabria, Av. Los Castros
s/n, 39005
Santander,
Spain.
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2 Technische Universität Chemnitz,
Faculty of Mathematics, Professorship Numerical Methods (Partial Differential Equations),
09107
Chemnitz,
Germany.
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;
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Received:
20
March
2015
Revised:
24
June
2015
Accepted:
10
September
2015
Abstract
Optimal control problems with semilinear parabolic state equations are considered. The objective features one out of three different terms promoting various spatio-temporal sparsity patterns of the control variable. For each problem, first-order necessary optimality conditions, as well as second-order necessary and sufficient optimality conditions are proved. The analysis includes the case in which the objective does not contain the squared norm of the control.
Mathematics Subject Classification: 49K20 / 49J52 / 35K58 / 65K10
Key words: Optimal control / directional sparsity / second-order optimality conditions / semilinear parabolic equations
The first author was partially supported by Spanish Ministerio de Economía y Competitividad under the project MTM2011-22711.
© EDP Sciences, SMAI 2016
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