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Erschienen in:
2007 | OriginalPaper | Buchkapitel
Fast Solution Techniques in Constrained Optimal Boundary Control of the Semilinear Heat Equation
verfasst von : M. Hintermüller, S. Volkwein, F. Diwoky
Erschienen in: Control of Coupled Partial Differential Equations
Verlag: Birkhäuser Basel
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Efficient numerical techniques for the solution of constrained optimal control problems for the nonlinear heat equation are considered. The nonlinearity in the governing equation is due to the boundary conditions which cover the Boltzmann radiation boundary condition. With respect to numerical algorithms, variants of semismooth Newton methods are proposed which allow a convergence analysis in function space. For the latter aspect the concept of generalized (Newton, or slant) differentiability is invoked. The paper ends with a comparison of the proposed algorithms among each other and with a sequential quadratic programming method.