On non-ergodic convergence rate of Douglas–Rachford alternating direction method of multipliers

Bingsheng He; Xiaoming Yuan

doi:10.1007/s00211-014-0673-6

On non-ergodic convergence rate of Douglas–Rachford alternating direction method of multipliers

Bingsheng He, Xiaoming Yuan^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

190 Citations (Scopus)

Abstract

This note proposes a novel approach to derive a worst-case O(1/k) convergence rate measured by the iteration complexity in a non-ergodic sense for the Douglas–Rachford alternating direction method of multipliers proposed by Glowinski and Marrocco.

Original language	English
Pages (from-to)	567–577
Number of pages	11
Journal	Numerische Mathematik
Volume	130
Issue number	3
Early online date	30 Nov 2014
DOIs	https://doi.org/10.1007/s00211-014-0673-6
Publication status	Published - Jul 2015

Scopus Subject Areas

Computational Mathematics
Applied Mathematics

Access to Document

10.1007/s00211-014-0673-6

Cite this

@article{3dab0b1ae05244f68139b21c1065f265,

title = "On non-ergodic convergence rate of Douglas–Rachford alternating direction method of multipliers",

abstract = "This note proposes a novel approach to derive a worst-case O(1/k) convergence rate measured by the iteration complexity in a non-ergodic sense for the Douglas–Rachford alternating direction method of multipliers proposed by Glowinski and Marrocco.",

author = "Bingsheng He and Xiaoming Yuan",

note = "Funding information: X. Yuan was supported by the General Research Fund from Hong Kong Research Grants Council: 203613. B. He was supported by the NSFC Grant 91130007 and 11471156. Publisher copyright: Copyright {\textcopyright} 2014, Springer-Verlag Berlin Heidelberg",

year = "2015",

month = jul,

doi = "10.1007/s00211-014-0673-6",

language = "English",

volume = "130",

pages = "567–577",

journal = "Numerische Mathematik",

issn = "0029-599X",

publisher = "Springer",

number = "3",

}

TY - JOUR

T1 - On non-ergodic convergence rate of Douglas–Rachford alternating direction method of multipliers

AU - He, Bingsheng

AU - Yuan, Xiaoming

N1 - Funding information: X. Yuan was supported by the General Research Fund from Hong Kong Research Grants Council: 203613. B. He was supported by the NSFC Grant 91130007 and 11471156. Publisher copyright: Copyright © 2014, Springer-Verlag Berlin Heidelberg

PY - 2015/7

Y1 - 2015/7

N2 - This note proposes a novel approach to derive a worst-case O(1/k) convergence rate measured by the iteration complexity in a non-ergodic sense for the Douglas–Rachford alternating direction method of multipliers proposed by Glowinski and Marrocco.

AB - This note proposes a novel approach to derive a worst-case O(1/k) convergence rate measured by the iteration complexity in a non-ergodic sense for the Douglas–Rachford alternating direction method of multipliers proposed by Glowinski and Marrocco.

UR - http://www.scopus.com/inward/record.url?scp=84912569509&partnerID=8YFLogxK

U2 - 10.1007/s00211-014-0673-6

DO - 10.1007/s00211-014-0673-6

M3 - Journal article

AN - SCOPUS:84912569509

SN - 0029-599X

VL - 130

SP - 567

EP - 577

JO - Numerische Mathematik

JF - Numerische Mathematik

IS - 3

ER -

On non-ergodic convergence rate of Douglas–Rachford alternating direction method of multipliers

Abstract

Scopus Subject Areas

Access to Document

Other files and links

Fingerprint

Cite this