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- state constraints (3)
- Nonlinear optimal control (2)
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- nonlocal radiation interface conditions (2)
- second-order sufficient conditions (2)
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- Lavrentiev type regularization (1)
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- C9 (13)
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- C (13)
A state-constrained optimal control problem arising in the context of sublimation crystal growth is considered. The presence of pointwise state-constraints and nonlocal radiation interface conditions
constitutes the major issue of this problem. A regularity result of the state is presented that allows to
derive the optimality condition.
A class of nonlinear elliptic optimal control
problems with mixed control-state constraints arising, e.g., in Lavrentiev-type
regularized state constrained optimal control is considered. Based
on its first order necessary optimality conditions, a semismooth
Newton method is proposed and its fast local convergence in
function space as well as a mesh-independence principle for
appropriate discretizations are proved. The paper ends by a
numerical verification of the theoretical results including a study of the
algorithm in the case of vanishing Lavrentiev-parameter. The latter process is
realized numerically by a combination of a nested iteration concept and an extrapolation technique for
the state with respect to the Lavrentiev-parameter.
Optimal control of 3D state-constrained induction heating problems with nonlocal radiation effects
(2009)
The paper is concerned with a class of optimal heating problems in semiconductor single crystal growth processes. To model the heating process, time-harmonic Maxwell equations are considered in the system of the state. Due to the high temperatures characterizing crystal growth, it is necessary to include nonlocal radiation boundary conditions and a temperature-dependent heat conductivity in the description of the heat transfer process. The first goal of this paper is to prove the existence and uniqueness of the solution to the state equation. The regularity analysis associated with the time harmonic Maxwell equations is also studied. In the second part of the paper, the existence and uniqueness of the solution to the corresponding linearized equation is shown. With this result at hand, the differentiability of the control-to-state mapping operator associated with the state equation is derived. Finally, based on the theoretical results, first oder necessary optimality conditi!
ons for an associated optimal control problem are established.