In this paper we are concerned with a distributed optimal control problem governed by an elliptic partial differential equation. State constraints of box type are considered. We show that the Lagrange multiplier associated with the state constraints, which is known to be a measure, is indeed more regular under quite general assumptions. We discretize the problem by continuous piecewise linear finite elements and we are able to prove that, for the case of a linear equation, the order of convergence for the error in L2(Ω) of the control variable is h | log h | in dimensions 2 and 3.
Mots clés : optimal control, state constraints, elliptic equations, Borel measures, error estimates
@article{COCV_2014__20_3_803_0,
author = {Casas, Eduardo and Mateos, Mariano and Vexler, Boris},
title = {New regularity results and improved error estimates for optimal control problems with state constraints},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {803--822},
publisher = {EDP-Sciences},
volume = {20},
number = {3},
year = {2014},
doi = {10.1051/cocv/2013084},
mrnumber = {3264224},
zbl = {1293.49044},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2013084/}
}
TY - JOUR AU - Casas, Eduardo AU - Mateos, Mariano AU - Vexler, Boris TI - New regularity results and improved error estimates for optimal control problems with state constraints JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2014 SP - 803 EP - 822 VL - 20 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2013084/ DO - 10.1051/cocv/2013084 LA - en ID - COCV_2014__20_3_803_0 ER -
%0 Journal Article %A Casas, Eduardo %A Mateos, Mariano %A Vexler, Boris %T New regularity results and improved error estimates for optimal control problems with state constraints %J ESAIM: Control, Optimisation and Calculus of Variations %D 2014 %P 803-822 %V 20 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2013084/ %R 10.1051/cocv/2013084 %G en %F COCV_2014__20_3_803_0
Casas, Eduardo; Mateos, Mariano; Vexler, Boris. New regularity results and improved error estimates for optimal control problems with state constraints. ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 3, pp. 803-822. doi : 10.1051/cocv/2013084. http://archive.numdam.org/articles/10.1051/cocv/2013084/
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