Geodesic
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

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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 L s -neighborhood of a reference function whereby the underlying analysis allows to use weaker norms than L ∞ .

DOI : 10.1051/cocv:2007028
Classification : 49K20, 35J65, 80M50
Keywords: optimal control, semilinear elliptic equations, nonlocal interface conditions, second-order sufficient optimality conditions 
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     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},
     mrnumber = {2351402},
     zbl = {1127.49020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2007028/}
}
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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

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