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Fast Solution Techniques in Constrained Optimal Boundary Control of the Semilinear Heat Equation

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2007

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Hintermüller, Michael
Diwoky, Franz

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https://doi.org/10.1007/978-3-7643-7721-2_6
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KUNISCH, Karl, ed. and others. Control of Coupled Partial Differential Equations. Basel: Birkhäuser, 2007, pp. 119-147. International Series of Numerical Mathematics. 155. ISBN 978-3-7643-7720-5. Available under: doi: 10.1007/978-3-7643-7721-2_6

Zusammenfassung

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.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

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Constrained optimal control, integral constraints, nonlinear heat equation, pointwise constraints, semismooth Newton

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ISO 690HINTERMÜLLER, Michael, Stefan VOLKWEIN, Franz DIWOKY, 2007. Fast Solution Techniques in Constrained Optimal Boundary Control of the Semilinear Heat Equation. In: KUNISCH, Karl, ed. and others. Control of Coupled Partial Differential Equations. Basel: Birkhäuser, 2007, pp. 119-147. International Series of Numerical Mathematics. 155. ISBN 978-3-7643-7720-5. Available under: doi: 10.1007/978-3-7643-7721-2_6
BibTex
@incollection{Hintermuller2007Solut-41215,
  year={2007},
  doi={10.1007/978-3-7643-7721-2_6},
  title={Fast Solution Techniques in Constrained Optimal Boundary Control of the Semilinear Heat Equation},
  number={155},
  isbn={978-3-7643-7720-5},
  publisher={Birkhäuser},
  address={Basel},
  series={International Series of Numerical Mathematics},
  booktitle={Control of Coupled Partial Differential Equations},
  pages={119--147},
  editor={Kunisch, Karl},
  author={Hintermüller, Michael and Volkwein, Stefan and Diwoky, Franz}
}
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