We consider a control constrained optimal control problem governed by a semilinear elliptic equation with nonlocal interface conditions. These conditions occur during the modeling of diffuse-gray conductive-radiative heat transfer. After stating first-order necessary conditions, second-order sufficient conditions are derived that account for strongly active sets. These conditions ensure local optimality in an -neighborhood of a reference function whereby the underlying analysis allows to use weaker norms than .
Classification : 49K20, 35J65, 80M50
Mots clés : optimal control, semilinear elliptic equations, nonlocal interface conditions, second-order sufficient optimality conditions
@article{COCV_2007__13_4_750_0,
author = {Meyer, Christian},
title = {Second-order sufficient optimality conditions for a semilinear optimal control problem with nonlocal radiation interface conditions},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {750--775},
publisher = {EDP-Sciences},
volume = {13},
number = {4},
year = {2007},
doi = {10.1051/cocv:2007028},
zbl = {1127.49020},
mrnumber = {2351402},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2007028/}
}
TY - JOUR AU - Meyer, Christian TI - Second-order sufficient optimality conditions for a semilinear optimal control problem with nonlocal radiation interface conditions JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2007 DA - 2007/// SP - 750 EP - 775 VL - 13 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2007028/ UR - https://zbmath.org/?q=an%3A1127.49020 UR - https://www.ams.org/mathscinet-getitem?mr=2351402 UR - https://doi.org/10.1051/cocv:2007028 DO - 10.1051/cocv:2007028 LA - en ID - COCV_2007__13_4_750_0 ER -
Meyer, Christian. Second-order sufficient optimality conditions for a semilinear optimal control problem with nonlocal radiation interface conditions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 4, pp. 750-775. doi : 10.1051/cocv:2007028. http://www.numdam.org/articles/10.1051/cocv:2007028/
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