A new inexact alternating directions method for monotone variational inequalities

Bingsheng He; Li Zhi Liao; Deren Han; Hai Yang

doi:10.1007/s101070100280

A new inexact alternating directions method for monotone variational inequalities

Bingsheng He^*, Li Zhi Liao, Deren Han, Hai Yang

^*Corresponding author for this work

Department of Mathematics

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

344 Citations (Scopus)

Abstract

The alternating directions method (ADM) is an effective method for solving a class of variational inequalities (VI) when the proximal and penalty parameters in sub-VI problems are properly selected. In this paper, we propose a new ADM method which needs to solve two strongly monotone sub-VI problems in each iteration approximately and allows the parameters to vary from iteration to iteration. The convergence of the proposed ADM method is proved under quite mild assumptions and flexible parameter conditions.

Original language	English
Pages (from-to)	103-118
Number of pages	16
Journal	Mathematical Programming
Volume	92
Issue number	1
DOIs	https://doi.org/10.1007/s101070100280
Publication status	Published - Mar 2002

Scopus Subject Areas

Software
General Mathematics

User-Defined Keywords

Alternating directions method
Inexact method
Variational inequality

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10.1007/s101070100280

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title = "A new inexact alternating directions method for monotone variational inequalities",

abstract = "The alternating directions method (ADM) is an effective method for solving a class of variational inequalities (VI) when the proximal and penalty parameters in sub-VI problems are properly selected. In this paper, we propose a new ADM method which needs to solve two strongly monotone sub-VI problems in each iteration approximately and allows the parameters to vary from iteration to iteration. The convergence of the proposed ADM method is proved under quite mild assumptions and flexible parameter conditions.",

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T1 - A new inexact alternating directions method for monotone variational inequalities

AU - He, Bingsheng

AU - Liao, Li Zhi

AU - Han, Deren

AU - Yang, Hai

PY - 2002/3

Y1 - 2002/3

N2 - The alternating directions method (ADM) is an effective method for solving a class of variational inequalities (VI) when the proximal and penalty parameters in sub-VI problems are properly selected. In this paper, we propose a new ADM method which needs to solve two strongly monotone sub-VI problems in each iteration approximately and allows the parameters to vary from iteration to iteration. The convergence of the proposed ADM method is proved under quite mild assumptions and flexible parameter conditions.

AB - The alternating directions method (ADM) is an effective method for solving a class of variational inequalities (VI) when the proximal and penalty parameters in sub-VI problems are properly selected. In this paper, we propose a new ADM method which needs to solve two strongly monotone sub-VI problems in each iteration approximately and allows the parameters to vary from iteration to iteration. The convergence of the proposed ADM method is proved under quite mild assumptions and flexible parameter conditions.

KW - Alternating directions method

KW - Inexact method

KW - Variational inequality

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DO - 10.1007/s101070100280

M3 - Journal article

AN - SCOPUS:0242462717

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SP - 103

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JO - Mathematical Programming

JF - Mathematical Programming

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ER -

A new inexact alternating directions method for monotone variational inequalities

Abstract

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