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 › Article › peer-review

158 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

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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",

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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.

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

Abstract

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