| 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.
eduardo.casas@unican.es
2 Technische Universität Chemnitz,
Faculty of Mathematics, Professorship Numerical Methods (Partial Differential Equations),
09107
Chemnitz,
Germany.
roland.herzog@mathematik.tu-chemnitz.de;
gerd.wachsmuth@mathematik.tu-chemnitz.de
Received:
20
March
2015
Revised:
24
June
2015
Accepted:
10
September
2015
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
© EDP Sciences, SMAI 2016
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.