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

Hintermüller, Michael; Volkwein, Stefan; Diwoky, Franz

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

Dateien

Zu diesem Dokument gibt es keine Dateien.

Datum

2007

Autor:innen

Hintermüller, Michael

Volkwein, Stefan

Diwoky, Franz

DOI (zitierfähiger Link)

https://doi.org/10.1007/978-3-7643-7721-2_6

Sammlungen

Mathematik und Statistik

Publikationstyp

Beitrag zu einem Sammelband

Publikationsstatus

Published

Erschienen 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

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.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

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

Zitieren

ISO 690

HINTERMÜLLER, 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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