A Note on the Alternating Direction Method of Multipliers

Deren Han, Xiaoming YUAN*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

161 Citations (Scopus)


We consider the linearly constrained separable convex programming, whose objective function is separable into m individual convex functions without coupled variables. The alternating direction method of multipliers has been well studied in the literature for the special case m=2, while it remains open whether its convergence can be extended to the general case m ≥3. This note shows the global convergence of this extension when the involved functions are further assumed to be strongly convex.

Original languageEnglish
Pages (from-to)227-238
Number of pages12
JournalJournal of Optimization Theory and Applications
Issue number1
Publication statusPublished - Oct 2012

Scopus Subject Areas

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

User-Defined Keywords

  • Alternating direction method of multipliers
  • Global convergence
  • Strongly convex functions


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