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

Published online by Cambridge University Press:  20 July 2007

Christian Meyer
Christian Meyer*
Affiliation:
WIAS - Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, D-10117 Berlin, Germany; cmeyer@math.tu-berlin.de
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Abstract

We consider a control constrained optimal control problem governed by a semilinear elliptic equation with nonlocal interface conditions. These conditions occur during themodeling 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 Ls -neighborhood of a reference function whereby the underlying analysis allows to use weaker norms than $L^\infty$ .

Keywords

Optimal controlsemilinear elliptic equationsnonlocal interface conditionssecond-order sufficient optimality conditions
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 13 , Issue 4 , October 2007 , pp. 750 - 775
Copyright
© EDP Sciences, SMAI, 2007

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