A Note on the Equivalence of Operator Splitting Methods

Walaa M. Moursi () and Yuriy Zinchenko ()
Additional contact information
Walaa M. Moursi: Stanford University, Electrical Engineering
Yuriy Zinchenko: University of Calgary, Department of Mathematics and Statistics

Chapter Chapter 13 in Splitting Algorithms, Modern Operator Theory, and Applications, 2019, pp 331-349 from Springer

Abstract: Abstract This note provides a comprehensive discussion of the equivalences between some splitting methods. We survey known results concerning these equivalences which have been studied over the past few decades. In particular, we provide simplified proofs of the equivalence of the ADMM and the Douglas–Rachford method and the equivalence of the ADMM with intermediate update of multipliers and the Peaceman–Rachford method.

Keywords: Alternating Direction Method of Multipliers (ADMM); Chambolle–Pock method; Douglas–Rachford algorithm; Dykstra method; Equivalence of splitting methods; Fenchel–Rockafellar duality; Peaceman–Rachford algorithm; 47H05; 47H09; 49M27; 49M29; 49N15; 90C25 (search for similar items in EconPapers)
Date: 2019
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-25939-6_13

Ordering information: This item can be ordered from
http://www.springer.com/9783030259396

DOI: 10.1007/978-3-030-25939-6_13

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().