A proximal point algorithm revisit on the alternating direction method of multipliers

Xing Ju Cai, Guo Yong Gu, Bing Sheng He, Xiaoming YUAN

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)

Abstract

The alternating direction method of multipliers (ADMM) is a benchmark for solving convex programming problems with separable objective functions and linear constraints. In the literature it has been illustrated as an application of the proximal point algorithm (PPA) to the dual problem of the model under consideration. This paper shows that ADMM can also be regarded as an application of PPA to the primal model with a customized choice of the proximal parameter. This primal illustration of ADMM is thus complemental to its dual illustration in the literature. This PPA revisit on ADMM from the primal perspective also enables us to recover the generalized ADMM proposed by Eckstein and Bertsekas easily. A worst-case O(1/t) convergence rate in ergodic sense is established for a slight extension of Eckstein and Bertsekas's generalized ADMM.

Original languageEnglish
Pages (from-to)2179-2186
Number of pages8
JournalScience China Mathematics
Volume56
Issue number10
DOIs
Publication statusPublished - Oct 2013

Scopus Subject Areas

  • Mathematics(all)

User-Defined Keywords

  • alternating direction method of multipliers
  • convergence rate
  • convex programming
  • proximal point algorithm

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