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- ItemRegularization of state-constrained elliptic optimal control problems with nonlocal radiation interface conditions(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Meyer, Christian; Yousept, IrwinA state-constrained optimal control problem with nonlocal radiation interface conditions arising from the modeling of crystal growth processes is considered. The problem is approximated by a Moreau-Yosida type regularization. Optimality conditions for the regularized problem are derived and the convergence of the regularized problems is shown. In the last part of the paper, some numerical results are presented.
- ItemState-constrained optimal control of semilinear elliptic equations with nonlocal radiation interface conditions(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Meyer, Christian; Yousept, IrwinWe consider a control- and state-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. The nonlocal radiation interface condition and the pointwise state-constraints represent the particular features of this problem. To deal with the state-constraints, continuity of the state is shown which allows to derive first-order necessary conditions. Afterwards, we establish second-order sufficient conditions that account for strongly active sets and ensure local optimality in an $L^2$-neighborhood.