Proximal point algorithms for general variational inequalities

M. Li; L. Z. Liao; X. M. Yuan

doi:10.1007/s10957-009-9532-5

Proximal point algorithms for general variational inequalities

M. Li, L. Z. Liao, X. M. Yuan

Department of Mathematics

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

10 Citations (Scopus)

31 Downloads (Pure)

Abstract

This paper presents a unified framework of proximal point algorithms (PPAs) for solving general variational inequalities (GVIs). Some existing PPAs for classical variational inequalities, including both the exact and inexact versions, are extended to solving GVIs. Consequently, several new PPA-based algorithms are proposed.

Original language	English
Pages (from-to)	125-145
Number of pages	21
Journal	Journal of Optimization Theory and Applications
Volume	142
Issue number	1
DOIs	https://doi.org/10.1007/s10957-009-9532-5
Publication status	Published - Jul 2009

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General variational inequality
Inexact versions
Proximal point algorithms

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10.1007/s10957-009-9532-5

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abstract = "This paper presents a unified framework of proximal point algorithms (PPAs) for solving general variational inequalities (GVIs). Some existing PPAs for classical variational inequalities, including both the exact and inexact versions, are extended to solving GVIs. Consequently, several new PPA-based algorithms are proposed.",

keywords = "General variational inequality, Inexact versions, Proximal point algorithms",

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

note = "Funding Information: M. Li was supported by NSFC Grant 10571083 and SRFDP Grant 200802861031. L.Z. Liao was supported in part by grants from Hong Kong Baptist University and the Research Grant Council of Hong Kong. X.M. Yuan was supported in part by FRG/08-09/II-40 from Hong Kong Baptist University and NSFC Grant 10701055.",

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AB - This paper presents a unified framework of proximal point algorithms (PPAs) for solving general variational inequalities (GVIs). Some existing PPAs for classical variational inequalities, including both the exact and inexact versions, are extended to solving GVIs. Consequently, several new PPA-based algorithms are proposed.

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KW - Inexact versions

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Proximal point algorithms for general variational inequalities

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