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Sufficient Optimality for Discretized Parabolic and Elliptic Control Problems

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Fast Solution of Discretized Optimization Problems

Part of the book series: ISNM International Series of Numerical Mathematics ((ISNM,volume 138))

Abstract

We study optimal control problems for semilinear parabolic and elliptic equations subject to control and state constraints. We quote known second-order sufficient optimality conditions (SSC) from the literature. Both problem classes are discretized by a finite difference method. The discrete SSC are stated and numerically verified for fine discretizations with the help of sparse linear algebra techniques. This confirms initial results reported earlier for such discretized control problems. In order to relate these results to optimality for the underlying continuous problems corresponding theoretical, especially convergence, results are still unavailable at present.

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Authors
  1. Hans D. Mittelmann
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Editors and Affiliations

  1. Center of Advanced European Studies and Research (caesar), Friedensplatz 16, Bonn, 53111, Germany

    Karl-Heinz Hoffmann

  2. Lehrstuhl für Angewandte Analysis mit Schwerpunkt Numerik, Universität Augsburg, Universitätsstr. 14, Augsburg, 86159, Germany

    Ronald H. W. Hoppe

  3. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, Berlin, 10117, Germany

    Volker Schulz

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© 2001 Springer Basel AG

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Mittelmann, H.D. (2001). Sufficient Optimality for Discretized Parabolic and Elliptic Control Problems. In: Hoffmann, KH., Hoppe, R.H.W., Schulz, V. (eds) Fast Solution of Discretized Optimization Problems. ISNM International Series of Numerical Mathematics, vol 138. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8233-0_14

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  • DOI: https://doi.org/10.1007/978-3-0348-8233-0_14

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9484-5

  • Online ISBN: 978-3-0348-8233-0

  • eBook Packages: Springer Book Archive

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