Local Linear Convergence of the Alternating Direction Method of Multipliers for Quadratic Programs

Deren Han; Xiaoming Yuan

doi:10.1137/120886753

Local Linear Convergence of the Alternating Direction Method of Multipliers for Quadratic Programs

Deren Han
, Xiaoming Yuan^*

^*Corresponding author for this work

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

107 Citations (Scopus)

120 Downloads (Pure)

Abstract

The Douglas-Rachford alternating direction method of multipliers (ADMM) has been widely used in various areas. The global convergence of ADMM is well known, while research on its convergence rate is still in its infancy. In this paper, we show the local linear convergence rate of ADMM for a quadratic program which includes some important applications of ADMM as special cases.

Original language	English
Pages (from-to)	3446-3457
Number of pages	12
Journal	SIAM Journal on Numerical Analysis
Volume	51
Issue number	6
DOIs	https://doi.org/10.1137/120886753
Publication status	Published - 17 Dec 2013

User-Defined Keywords

Alternating direction method of multipliers
Error bound
Linear convergence rate
Quadratic program

Access to Document

10.1137/120886753

Full TextFinal published version, 192 KB

Cite this

@article{e9243438137740bc85141829bc115c20,

title = "Local Linear Convergence of the Alternating Direction Method of Multipliers for Quadratic Programs",

abstract = "The Douglas-Rachford alternating direction method of multipliers (ADMM) has been widely used in various areas. The global convergence of ADMM is well known, while research on its convergence rate is still in its infancy. In this paper, we show the local linear convergence rate of ADMM for a quadratic program which includes some important applications of ADMM as special cases.",

keywords = "Alternating direction method of multipliers, Error bound, Linear convergence rate, Quadratic program",

author = "Deren Han and Xiaoming Yuan",

note = "Funding information: School of Mathematical Sciences, Key Laboratory for NSLSCS of Jiangsu Province, Nanjing Normal University, Nanjing 210046, People{\textquoteright}s Republic of China ([email protected]). This author was supported by NSFC grants 11071122 and 11171159. \$ Department of Mathematics, Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Hong Kong, People{\textquoteright}s Republic of China ([email protected]). This author was supported by the General Research Fund from Hong Kong Research Grants Council: 203613. Publisher copyright: {\textcopyright} 2013, Society for Industrial and Applied Mathematics",

year = "2013",

month = dec,

day = "17",

doi = "10.1137/120886753",

language = "English",

volume = "51",

pages = "3446--3457",

journal = "SIAM Journal on Numerical Analysis",

issn = "0036-1429",

publisher = "Society for Industrial and Applied Mathematics (SIAM)",

number = "6",

}

TY - JOUR

T1 - Local Linear Convergence of the Alternating Direction Method of Multipliers for Quadratic Programs

AU - Han, Deren

AU - Yuan, Xiaoming

N1 - Funding information: School of Mathematical Sciences, Key Laboratory for NSLSCS of Jiangsu Province, Nanjing Normal University, Nanjing 210046, People’s Republic of China ([email protected]). This author was supported by NSFC grants 11071122 and 11171159. $ Department of Mathematics, Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Hong Kong, People’s Republic of China ([email protected]). This author was supported by the General Research Fund from Hong Kong Research Grants Council: 203613. Publisher copyright: © 2013, Society for Industrial and Applied Mathematics

PY - 2013/12/17

Y1 - 2013/12/17

N2 - The Douglas-Rachford alternating direction method of multipliers (ADMM) has been widely used in various areas. The global convergence of ADMM is well known, while research on its convergence rate is still in its infancy. In this paper, we show the local linear convergence rate of ADMM for a quadratic program which includes some important applications of ADMM as special cases.

AB - The Douglas-Rachford alternating direction method of multipliers (ADMM) has been widely used in various areas. The global convergence of ADMM is well known, while research on its convergence rate is still in its infancy. In this paper, we show the local linear convergence rate of ADMM for a quadratic program which includes some important applications of ADMM as special cases.

KW - Alternating direction method of multipliers

KW - Error bound

KW - Linear convergence rate

KW - Quadratic program

UR - https://www.scopus.com/pages/publications/84892949395

U2 - 10.1137/120886753

DO - 10.1137/120886753

M3 - Journal article

AN - SCOPUS:84892949395

SN - 0036-1429

VL - 51

SP - 3446

EP - 3457

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 6

ER -

Local Linear Convergence of the Alternating Direction Method of Multipliers for Quadratic Programs

Abstract

User-Defined Keywords

Access to Document

Other files and links

Fingerprint

Cite this