Inexact Alternating Direction Methods of Multipliers with Logarithmic-Quadratic Proximal Regularization

Min Li, Lizhi LIAO, Xiaoming YUAN*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

In the literature, it was shown recently that the Douglas-Rachford alternating direction method of multipliers can be combined with the logarithmic-quadratic proximal regularization for solving a class of variational inequalities with separable structures. This paper studies the inexact version of this combination, where the resulting subproblems are allowed to be solved approximately subject to different inexactness criteria. We prove the global convergence and establish worst-case convergence rates for the derived inexact algorithms.

Original languageEnglish
Pages (from-to)412-436
Number of pages25
JournalJournal of Optimization Theory and Applications
Volume159
Issue number2
DOIs
Publication statusPublished - Nov 2013

Scopus Subject Areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

User-Defined Keywords

  • Alternating direction method of multipliers
  • Convergence rate
  • Inexact
  • Logarithmic-quadratic proximal regularization
  • Variational inequality

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