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Proximal Point Algorithms for General Variational Inequalities

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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.

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Authors and Affiliations

  1. Department of Management Science and Engineering, School of Economics and Management, Southeast University, Nanjing, 210096, China

    M. Li

  2. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China

    L. Z. Liao & X. M. Yuan

Authors
  1. M. Li
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  2. L. Z. Liao
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  3. X. M. Yuan
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Corresponding author

Correspondence to X. M. Yuan.

Additional information

Communicated by P.M. Pardalos.

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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Li, M., Liao, L.Z. & Yuan, X.M. Proximal Point Algorithms for General Variational Inequalities. J Optim Theory Appl 142, 125–145 (2009). https://doi.org/10.1007/s10957-009-9532-5

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