This paper deals with the numerical solution of optimal control problems with control complementarity constraints. For that purpose, we suggest the use of several penalty methods which differ with respect to the handling of the complementarity constraint which is either penalized as a whole with the aid of NCP-functions or decoupled in such a way that non-negativity constraints as well as the equilibrium condition are penalized individually. We first present general global and local convergence results which cover several different penalty schemes before two decoupled methods which are based on a classical ℓ1- and ℓ2-penalty term, respectively, are investigated in more detail. Afterwards, the numerical implementation of these penalty methods is discussed. Based on some examples, where the optimal boundary control of a parabolic partial differential equation is considered, some quantitative properties of the resulting algorithms are compared.
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Keywords: Complementarity constraints, optimal control, parabolic PDE, penalty method
@article{COCV_2021__27_1_A47_0,
author = {Deng, Yu and Mehlitz, Patrick and Pr\"ufert, Uwe},
title = {Coupled \protect\emph{versus} decoupled penalization of control complementarity constraints},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021022},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021022/}
}
TY - JOUR AU - Deng, Yu AU - Mehlitz, Patrick AU - Prüfert, Uwe TI - Coupled versus decoupled penalization of control complementarity 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/2021022/ DO - 10.1051/cocv/2021022 LA - en ID - COCV_2021__27_1_A47_0 ER -
%0 Journal Article %A Deng, Yu %A Mehlitz, Patrick %A Prüfert, Uwe %T Coupled versus decoupled penalization of control complementarity 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/2021022/ %R 10.1051/cocv/2021022 %G en %F COCV_2021__27_1_A47_0
Deng, Yu; Mehlitz, Patrick; Prüfert, Uwe. Coupled versus decoupled penalization of control complementarity constraints. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 45. doi: 10.1051/cocv/2021022
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