On the O(1/N) convergence rate of the Douglas-Rachford alternating direction method

Bingsheng He*, Xiaoming YUAN

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

491 Citations (Scopus)

Abstract

Alternating direction methods (ADMs) have been well studied in the literature, and they have found many efficient applications in various fields. In this note, we focus on the Douglas- Rachford ADM scheme proposed by Glowinski and Marrocco, and we aim at providing a simple approach to estimating its convergence rate in terms of the iteration number. The linearized version of this ADM scheme, which is known as the split inexact Uzawa method in the image processing literature, is also discussed.

Original languageEnglish
Pages (from-to)700-709
Number of pages10
JournalSIAM Journal on Numerical Analysis
Volume50
Issue number2
DOIs
Publication statusPublished - 2012

Scopus Subject Areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Alternating direction method
  • Convergence rate
  • Convex programming
  • Split inexact Uzawa method
  • Variational inequalities

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