We prove first- and second-order optimality conditions for sparse, purely time-dependent optimal control problems governed by a quasilinear parabolic PDE. In particular, we analyze sparsity patterns of the optimal controls induced by different sparsity enforcing functionals in the purely timedependent control case and illustrate them by numerical examples. Our findings are based on results obtained by abstraction of well known techniques from the literature.
Keywords: Optimal control, (directional) sparsity, purely time-dependent control, second-order optimality conditions, quasilinear parabolic equations
@article{COCV_2022__28_1_A68_0,
author = {Hoppe, Fabian and Neitzel, Ira},
title = {Purely time-dependent optimal control of quasilinear parabolic {PDEs} with sparsity enforcing penalization},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2022},
publisher = {EDP-Sciences},
volume = {28},
doi = {10.1051/cocv/2022058},
mrnumber = {4504127},
zbl = {1509.49013},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2022058/}
}
TY - JOUR AU - Hoppe, Fabian AU - Neitzel, Ira TI - Purely time-dependent optimal control of quasilinear parabolic PDEs with sparsity enforcing penalization JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2022 VL - 28 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2022058/ DO - 10.1051/cocv/2022058 LA - en ID - COCV_2022__28_1_A68_0 ER -
%0 Journal Article %A Hoppe, Fabian %A Neitzel, Ira %T Purely time-dependent optimal control of quasilinear parabolic PDEs with sparsity enforcing penalization %J ESAIM: Control, Optimisation and Calculus of Variations %D 2022 %V 28 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2022058/ %R 10.1051/cocv/2022058 %G en %F COCV_2022__28_1_A68_0
Hoppe, Fabian; Neitzel, Ira. Purely time-dependent optimal control of quasilinear parabolic PDEs with sparsity enforcing penalization. ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 68. doi: 10.1051/cocv/2022058
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