Second-order sufficient optimality conditions for a semilinear optimal control problem with nonlocal radiation interface conditions. (English) Zbl 1127.49020

Meyer, Christian

ESAIM, Control Optim. Calc. Var. 13, No. 4, 750-775 (2007).

Summary: 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 \(L^\infty\).

MSC:

49K20	Optimality conditions for problems involving partial differential equations
35J65	Nonlinear boundary value problems for linear elliptic equations
80M50	Optimization problems in thermodynamics and heat transfer
35B37	PDE in connection with control problems (MSC2000)

Keywords:

optimal control; semilinear elliptic equations; nonlocal interface conditions; second-order sufficient optimality conditions

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