Semismooth newton and augmented lagrangian methods for a simplified friction problem

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Abstract

In this paper a simplified friction problem and iterative second-order algorithms for its solution are analyzed in infinite dimensional function spaces. Motivated from the dual formulation, a primal-dual active set strategy and a semismooth Newton method for a regularized problem as well as an augmented Lagrangian method for the original problem are presented and their close relation is analyzed. Local as well as global convergence results are given. By means of numerical tests, we discuss among others convergence properties, the dependence on the mesh, and the role of the regularization and illustrate the efficiency of the proposed methodologies.

Original languageEnglish (US)
Pages (from-to)39-62
Number of pages24
JournalSIAM Journal on Optimization
Volume15
Issue number1
DOIs
StatePublished - 2005

Keywords

  • Augmented Lagrangians
  • Friction problem
  • Primaldual active set algorithm
  • Semismooth Newton method

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science

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