Optimal control problems for semilinear elliptic equations with control constraints and pointwise state constraints are studied. Several theoretical results are derived, which are necessary to carry out a numerical analysis for this class of control problems. In particular, sufficient second-order optimality conditions, some new regularity results on optimal controls and a sufficient condition for the uniqueness of the Lagrange multiplier associated with the state constraints are presented.
Mots-clés : optimal control, pointwise state constraints, first and second order optimality conditions, Lagrange multipliers, Borel measures
@article{COCV_2010__16_3_581_0,
author = {Casas, Eduardo and Tr\"oltzsch, Fredi},
title = {Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {581--600},
publisher = {EDP-Sciences},
volume = {16},
number = {3},
year = {2010},
doi = {10.1051/cocv/2009010},
mrnumber = {2674627},
zbl = {1201.49004},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2009010/}
}
TY - JOUR AU - Casas, Eduardo AU - Tröltzsch, Fredi TI - Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2010 SP - 581 EP - 600 VL - 16 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2009010/ DO - 10.1051/cocv/2009010 LA - en ID - COCV_2010__16_3_581_0 ER -
%0 Journal Article %A Casas, Eduardo %A Tröltzsch, Fredi %T Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2010 %P 581-600 %V 16 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2009010/ %R 10.1051/cocv/2009010 %G en %F COCV_2010__16_3_581_0
Casas, Eduardo; Tröltzsch, Fredi. Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 3, pp. 581-600. doi : 10.1051/cocv/2009010. http://www.numdam.org/articles/10.1051/cocv/2009010/
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