Mathematical Programming

, Volume 101, Issue 1, pp 151–184 | Cite as

A mesh-independence result for semismooth Newton methods

Article

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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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.University of GrazDepartment of MathematicsGrazAustria
  2. 2.Rice UniversityDepartment of Computational and Applied MathematicsHoustonUSA
  3. 3.Universität HamburgFachbereich Mathematik, Schwerpunkt Optimierung und ApproximationHamburgGermany

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