The improvement with relative errors of He et al.'s inexact alternating direction method for monotone variational inequalities

Xiao-Ming Yuan

doi:10.1016/j.mcm.2005.04.007

The improvement with relative errors of He et al.'s inexact alternating direction method for monotone variational inequalities

Xiao-Ming Yuan

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

8 Citations (Scopus)

Abstract

The proximal alternating direction method (PADM) solves a kind of structured monotone variational inequalities (VI) via solving a series of lower-dimensional and strongly monotone sub-VIs. We present a new inexact PADM which solves the involved sub-VIs approximately. The new criteria for solving the involved sub-VIs approximately are relaxed than those presented by He et al. [1]. In addition, the new criteria make use of the relative errors of each iteration instead of the absolute errors to control the accuracy of the inexact solutions of the sub-VIs. © 2005 Elsevier Ltd. All rights reserved.

Original language	English
Pages (from-to)	1225-1236
Journal	Mathematical and Computer Modelling
Volume	42
Issue number	11-12
DOIs	https://doi.org/10.1016/j.mcm.2005.04.007
Publication status	Published - Dec 2005

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Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Research Keywords

Alternating direction method
Inexact criterion
Monotone variational inequalities
Proximal point method
Relative error

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title = "The improvement with relative errors of He et al.'s inexact alternating direction method for monotone variational inequalities",

abstract = "The proximal alternating direction method (PADM) solves a kind of structured monotone variational inequalities (VI) via solving a series of lower-dimensional and strongly monotone sub-VIs. We present a new inexact PADM which solves the involved sub-VIs approximately. The new criteria for solving the involved sub-VIs approximately are relaxed than those presented by He et al. [1]. In addition, the new criteria make use of the relative errors of each iteration instead of the absolute errors to control the accuracy of the inexact solutions of the sub-VIs. {\textcopyright} 2005 Elsevier Ltd. All rights reserved.",

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author = "Xiao-Ming Yuan",

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AU - Yuan, Xiao-Ming

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

PY - 2005/12

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N2 - The proximal alternating direction method (PADM) solves a kind of structured monotone variational inequalities (VI) via solving a series of lower-dimensional and strongly monotone sub-VIs. We present a new inexact PADM which solves the involved sub-VIs approximately. The new criteria for solving the involved sub-VIs approximately are relaxed than those presented by He et al. [1]. In addition, the new criteria make use of the relative errors of each iteration instead of the absolute errors to control the accuracy of the inexact solutions of the sub-VIs. © 2005 Elsevier Ltd. All rights reserved.

AB - The proximal alternating direction method (PADM) solves a kind of structured monotone variational inequalities (VI) via solving a series of lower-dimensional and strongly monotone sub-VIs. We present a new inexact PADM which solves the involved sub-VIs approximately. The new criteria for solving the involved sub-VIs approximately are relaxed than those presented by He et al. [1]. In addition, the new criteria make use of the relative errors of each iteration instead of the absolute errors to control the accuracy of the inexact solutions of the sub-VIs. © 2005 Elsevier Ltd. All rights reserved.

KW - Alternating direction method

KW - Inexact criterion

KW - Monotone variational inequalities

KW - Proximal point method

KW - Relative error

UR - https://www.scopus.com/pages/publications/28844506079

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-28844506079&origin=recordpage

U2 - 10.1016/j.mcm.2005.04.007

DO - 10.1016/j.mcm.2005.04.007

M3 - RGC 21 - Publication in refereed journal

SN - 0895-7177

VL - 42

SP - 1225

EP - 1236

JO - Mathematical and Computer Modelling

JF - Mathematical and Computer Modelling

IS - 11-12

ER -

The improvement with relative errors of He et al.'s inexact alternating direction method for monotone variational inequalities

Abstract

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