State-constrained optimal control of semilinear elliptic equations with nonlocal radiation interface conditions
- Meyer, Christian
- Yousept, Irwin
2010 Mathematics Subject Classification
- 35J60 49K20 49M05 65K10
- Nonlinear optimal control, nonlocal radiation interface conditions, state constraints, first-order necessary conditions, second-order sufficient conditions
We 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.
- SIAM J. Control Optim., 48 (2009) pp. 734--755