We establish some second order necessary conditions for optimal control problems of evolution equations involving final point equality and inequality constraints. Compared with the existing works, the main difference is due to the presence of end-point equality constraints. With such constraints, we cannot simply use the variational techniques since perturbations of a given control may be no longer admissible. We also cannot use the Ekeland’s variational principle, which is a first order variational principle, to obtain second order necessary conditions. Instead, we combine some inverse mapping theorems on metric spaces and second order linearization of data to obtain our results.
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Keywords: Optimal control, time evolution partial differential equation, second order necessary condition, local minimizer
@article{COCV_2021__27_1_A73_0,
author = {Frankowska, H\'el\`ene and L\"u, Qi},
editor = {Buttazzo, G. and Casas, E. and de Teresa, L. and Glowinski, R. and Leugering, G. and Tr\'elat, E. and Zhang, X.},
title = {Second order necessary conditions for optimal control problems of evolution equations involving final point equality constraints},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021065},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021065/}
}
TY - JOUR AU - Frankowska, Hélène AU - Lü, Qi ED - Buttazzo, G. ED - Casas, E. ED - de Teresa, L. ED - Glowinski, R. ED - Leugering, G. ED - Trélat, E. ED - Zhang, X. TI - Second order necessary conditions for optimal control problems of evolution equations involving final point equality constraints JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021065/ DO - 10.1051/cocv/2021065 LA - en ID - COCV_2021__27_1_A73_0 ER -
%0 Journal Article %A Frankowska, Hélène %A Lü, Qi %E Buttazzo, G. %E Casas, E. %E de Teresa, L. %E Glowinski, R. %E Leugering, G. %E Trélat, E. %E Zhang, X. %T Second order necessary conditions for optimal control problems of evolution equations involving final point equality constraints %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021065/ %R 10.1051/cocv/2021065 %G en %F COCV_2021__27_1_A73_0
Frankowska, Hélène; Lü, Qi. Second order necessary conditions for optimal control problems of evolution equations involving final point equality constraints. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 71. doi: 10.1051/cocv/2021065
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