Some proximal algorithms for linearly constrained general variational inequalities

M. Li; X. M. Yuan

doi:10.1080/02331934.2010.522714

Some proximal algorithms for linearly constrained general variational inequalities

M. Li, X. M. Yuan

Department of Mathematics

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

Abstract

Based on the classical proximal point algorithm (PPA), some PPA-based numerical algorithms for general variational inequalities (GVIs) have been developed recently. Inspired by these algorithms, in this article we propose some proximal algorithms for solving linearly constrained GVIs (LCGVIs). The resulted subproblems are regularized proximally, and they are allowed to be solved either exactly or approximately.

Original language	English
Pages (from-to)	505-524
Number of pages	20
Journal	Optimization
Volume	61
Issue number	5
DOIs	https://doi.org/10.1080/02331934.2010.522714
Publication status	Published - May 2012

Scopus Subject Areas

Control and Optimization
Management Science and Operations Research
Applied Mathematics

User-Defined Keywords

general variational inequality
inexact methods
linear constraint
proximal point algorithm

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10.1080/02331934.2010.522714

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title = "Some proximal algorithms for linearly constrained general variational inequalities",

abstract = "Based on the classical proximal point algorithm (PPA), some PPA-based numerical algorithms for general variational inequalities (GVIs) have been developed recently. Inspired by these algorithms, in this article we propose some proximal algorithms for solving linearly constrained GVIs (LCGVIs). The resulted subproblems are regularized proximally, and they are allowed to be solved either exactly or approximately.",

keywords = "general variational inequality, inexact methods, linear constraint, proximal point algorithm",

author = "M. Li and Yuan, {X. M.}",

note = "Funding Information: M. Li was supported by Social Sciences Foundation by the State Education Commission 09YJA630020, the NSFC grant 10926147 and 11001053. X.M. Yuan was supported in part by FRG/08-09/II-40 from Hong Kong Baptist University and the NSFC grant 10701055.",

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AU - Yuan, X. M.

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N2 - Based on the classical proximal point algorithm (PPA), some PPA-based numerical algorithms for general variational inequalities (GVIs) have been developed recently. Inspired by these algorithms, in this article we propose some proximal algorithms for solving linearly constrained GVIs (LCGVIs). The resulted subproblems are regularized proximally, and they are allowed to be solved either exactly or approximately.

AB - Based on the classical proximal point algorithm (PPA), some PPA-based numerical algorithms for general variational inequalities (GVIs) have been developed recently. Inspired by these algorithms, in this article we propose some proximal algorithms for solving linearly constrained GVIs (LCGVIs). The resulted subproblems are regularized proximally, and they are allowed to be solved either exactly or approximately.

KW - general variational inequality

KW - inexact methods

KW - linear constraint

KW - proximal point algorithm

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DO - 10.1080/02331934.2010.522714

M3 - Journal article

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SP - 505

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JO - Optimization

JF - Optimization

IS - 5

ER -

Some proximal algorithms for linearly constrained general variational inequalities

Abstract

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