Further Study on the Convergence Rate of Alternating Direction Method of Multipliers with Logarithmic-quadratic Proximal Regularization

Caihua Chen, Min Li, Xiaoming YUAN*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In the literature, the combination of the alternating direction method of multipliers with the logarithmic-quadratic proximal regularization has been proved to be convergent, and its worst-case convergence rate in the ergodic sense has been established. In this paper, we focus on a convex minimization model and consider an inexact version of the combination of the alternating direction method of multipliers with the logarithmic-quadratic proximal regularization. Our primary purpose is to further study its convergence rate and to establish its worst-case convergence rates measured by the iteration complexity in both the ergodic and non-ergodic senses. In particular, existing convergence rate results for this combination are subsumed by the new results.

Original languageEnglish
Pages (from-to)906-929
Number of pages24
JournalJournal of Optimization Theory and Applications
Volume166
Issue number3
DOIs
Publication statusPublished - 3 Sep 2015

Scopus Subject Areas

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

User-Defined Keywords

  • Alternating direction method of multipliers
  • Convergence rate
  • Convex programming
  • Iteration complexity
  • Logarithmic-quadratic proximal

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