Convergence Analysis of the Generalized Alternating Direction Method of Multipliers with Logarithmic–Quadratic Proximal Regularization

Min Li, Xinxin Li, Xiaoming YUAN*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

We consider combining the generalized alternating direction method of multipliers, proposed by Eckstein and Bertsekas, with the logarithmic–quadratic proximal method proposed by Auslender, Teboulle, and Ben-Tiba for solving a variational inequality with separable structures. For the derived algorithm, we prove its global convergence and establish its worst-case convergence rate measured by the iteration complexity in both the ergodic and nonergodic senses.

Original languageEnglish
Pages (from-to)218-233
Number of pages16
JournalJournal of Optimization Theory and Applications
Volume164
Issue number1
DOIs
Publication statusPublished - Jan 2014

Scopus Subject Areas

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

User-Defined Keywords

  • Convergence rate
  • Generalized alternating direction method of multipliers
  • Logarithmic–quadratic proximal method
  • Variational inequality

Fingerprint

Dive into the research topics of 'Convergence Analysis of the Generalized Alternating Direction Method of Multipliers with Logarithmic–Quadratic Proximal Regularization'. Together they form a unique fingerprint.

Cite this