Second-order sufficient optimality conditions for a semilinear optimal control problem with nonlocal radiation interface conditions

Abstract

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 ∞ .