SECOND-ORDER SUFFICIENT OPTIMALITY CONDITIONS FOR A SEMILINEAR OPTIMAL CONTROL PROBLEM WITH NONLOCAL RADIATION INTERFACE CONDITIONS

摘要

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~∞.