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Truncated Nonsmooth Newton Multigrid Methods for Convex Minimization Problems

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Domain Decomposition Methods in Science and Engineering XVIII

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 70))

Summary

We present a new inexact nonsmooth Newton method for the solution of convex minimization problems with piecewise smooth, pointwise nonlinearities. The algorithm consists of a nonlinear smoothing step on the fine level and a linear coarse correction. Suitable postprocessing guarantees global convergence even in the case of a single multigrid step for each linear subproblem. Numerical examples show that the overall efficiency is comparable to multigrid for similar linear problems.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Freie Universität Berlin, Berlin, Germany

    Carsten Gräser, Uli Sack & Oliver Sander

  2. DFG Research Center MATHEON, Berlin, Germany

    Carsten Gräser, Uli Sack & Oliver Sander

Authors
  1. Carsten Gräser
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  2. Uli Sack
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  3. Oliver Sander
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Corresponding author

Correspondence to Carsten Gräser .

Editor information

Editors and Affiliations

  1. School of Computer Science and Engineering, The Hebrew University of Jerusalem, Ross Building - Givat Ram Campus, 91904, Jerusalem, Israel

    Michel Bercovier

  2. Section de mathématiques, Université de Genève, 2-4 rue du Lièvre, 1211, Genève 24, Switzerland

    Martin J. Gander

  3. Institut für Mathematik, Freie Universität Berlin, Arnimallee 6, 14195, Berlin-Dahlem, Germany

    Ralf Kornhuber

  4. Courant Institute, 251 Mercer Street, New York, NY, 10012, USA

    Olof Widlund

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© 2009 Springer-Verlag Berlin Heidelberg

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Gräser, C., Sack, U., Sander, O. (2009). Truncated Nonsmooth Newton Multigrid Methods for Convex Minimization Problems. In: Bercovier, M., Gander, M.J., Kornhuber, R., Widlund, O. (eds) Domain Decomposition Methods in Science and Engineering XVIII. Lecture Notes in Computational Science and Engineering, vol 70. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02677-5_12

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