We analyze an optimal control problem for the stationary two-dimensional Boussinesq system with controls taken in the space of regular Borel measures. Such measure-valued controls are known to produce sparse solutions. First-order and second-order necessary and sufficient optimality conditions are established. Following an optimize-then-discretize strategy, the corresponding finite element approximation will be solved by a semi-smooth Newton method initialized by a continuation strategy. The controls are discretized by finite linear combinations of Dirac measures concentrated at the nodes associated with the degrees of freedom for the mini-finite element.
Keywords: Boussinesq system, Borel measures, Sparse controls, optimality conditions, finite elements, semi-smooth Newton algorithm
@article{COCV_2022__28_1_A22_0,
author = {Peralta, Gilbert},
title = {Optimal {Borel} measure controls for the two-dimensional stationary {Boussinesq} system},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2022},
publisher = {EDP-Sciences},
volume = {28},
doi = {10.1051/cocv/2022016},
mrnumber = {4395150},
zbl = {1485.49011},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2022016/}
}
TY - JOUR AU - Peralta, Gilbert TI - Optimal Borel measure controls for the two-dimensional stationary Boussinesq system JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2022 VL - 28 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2022016/ DO - 10.1051/cocv/2022016 LA - en ID - COCV_2022__28_1_A22_0 ER -
%0 Journal Article %A Peralta, Gilbert %T Optimal Borel measure controls for the two-dimensional stationary Boussinesq system %J ESAIM: Control, Optimisation and Calculus of Variations %D 2022 %V 28 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2022016/ %R 10.1051/cocv/2022016 %G en %F COCV_2022__28_1_A22_0
Peralta, Gilbert. Optimal Borel measure controls for the two-dimensional stationary Boussinesq system. ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 22. doi: 10.1051/cocv/2022016
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