Global and superlinear convergence of inexact Uzawa methods for saddle point problems with nondifferentiable mappings

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Abstract

This paper investigates inexact Uzawa methods for nonlinear saddle point problems. We prove that the inexact Uzawa method converges globally and superlinearly even if the derivative of the nonlinear mapping does not exist. We show that the Newton-type decomposition method for saddle point problems is a special case of a Newton-Uzawa method. We discuss applications of inexact Uzawa methods to separable convex programming problems and coupling of finite elements/boundary elements for nonlinear interface problems.
Original languageEnglish
Pages (from-to)1130-1148
Number of pages19
JournalSIAM Journal on Numerical Analysis
Volume35
Issue number3
DOIs
Publication statusPublished - 1 Jan 1998
Externally publishedYes

Keywords

  • Convergence
  • Inexact
  • Inner/outer
  • Newton
  • Nonsmooth
  • Saddle point
  • Uzawa

ASJC Scopus subject areas

  • Numerical Analysis

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