On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators

Jonathan Eckstein, Dimitri P. Bertsekas

Research output: Contribution to journalArticlepeer-review

693 Scopus citations

Abstract

This paper shows, by means of an operator called a splitting operator, that the Douglas-Rachford splitting method for finding a zero of the sum of two monotone operators is a special case of the proximal point algorithm. Therefore, applications of Douglas-Rachford splitting, such as the alternating direction method of multipliers for convex programming decomposition, are also special cases of the proximal point algorithm. This observation allows the unification and generalization of a variety of convex programming algorithms. By introducing a modified version of the proximal point algorithm, we derive a new, generalized alternating direction method of multipliers for convex programming. Advances of this sort illustrate the power and generality gained by adopting monotone operator theory as a conceptual framework.

Original languageEnglish (US)
Pages (from-to)293-318
Number of pages26
JournalMathematical Programming
Volume55
Issue number3
StatePublished - Jul 6 1992
Externally publishedYes

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

Fingerprint Dive into the research topics of 'On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators'. Together they form a unique fingerprint.

Cite this