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A mesh-independence result for semismooth Newton methods

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Abstract.

For a class of semismooth operator equations a mesh independence result for generalized Newton methods is established. The main result states that the continuous and the discrete Newton process, when initialized properly, converge q-linearly with the same rate. The problem class considered in the paper includes MCP-function based reformulations of first order conditions of a class of control constrained optimal control problems for partial differential equations for which a numerical validation of the theoretical results is given.

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Authors and Affiliations

  1. University of Graz, Department of Mathematics, Heinrichstr. 36, A-8010, Graz, Austria

    Michael Hintermüller

  2. Rice University, Department of Computational and Applied Mathematics, - MS134, 6100 S. Main Street, Houston, TX, 77005, USA

    Michael Hintermüller

  3. Universität Hamburg, Fachbereich Mathematik, Schwerpunkt Optimierung und Approximation, Bundesstr. 55, 20146, Hamburg, Germany

    Michael Ulbrich

Authors
  1. Michael Hintermüller
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  2. Michael Ulbrich
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Correspondence to Michael Ulbrich.

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Mathematics Subject Classification (1991):65J15, 65K10, 49M25, 90C33

Accepted: April 19, 2004

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Hintermüller, M., Ulbrich, M. A mesh-independence result for semismooth Newton methods. Math. Program., Ser. A 101, 151–184 (2004). https://doi.org/10.1007/s10107-004-0540-9

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  • DOI: https://doi.org/10.1007/s10107-004-0540-9

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