Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems
ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 3, p. 581-600

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.

DOI : https://doi.org/10.1051/cocv/2009010
Classification:  49J20,  49K20,  35J65
Keywords: 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},
publisher = {EDP-Sciences},
volume = {16},
number = {3},
year = {2010},
pages = {581-600},
doi = {10.1051/cocv/2009010},
zbl = {1201.49004},
mrnumber = {2674627},
language = {en},
url = {http://www.numdam.org/item/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, Volume 16 (2010) no. 3, pp. 581-600. doi : 10.1051/cocv/2009010. http://www.numdam.org/item/COCV_2010__16_3_581_0/

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