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A Logarithmic-Quadratic Proximal Prediction-Correction Method for Structured Monotone Variational Inequalities

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Abstract

Inspired by the Logarithmic-Quadratic Proximal (LQP) method for variational inequalities, we present a prediction-correction method for structured monotone variational inequalities. Each iteration of the new method consists of a prediction and a correction. Both the predictor and the corrector are obtained easily with tiny computational load. In particular, the LQP system that appears in the prediction is approximately solved under significantly relaxed inexactness restriction. Global convergence of the new method is proved under mild assumptions. In addition, we present a self-adaptive version of the new method that leads to easier implementations. Preliminary numerical experiments for traffic equilibrium problems indicate that the new method is effectively applicable in practice.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, 210093, China

    Bing-Sheng He & Ya Xu

  2. Department of Mathematics, City University of Hong Kong, Hong Kong, China

    Xiao-Ming Yuan

Authors
  1. Bing-Sheng He
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  2. Ya Xu
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  3. Xiao-Ming Yuan
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Corresponding author

Correspondence to Bing-Sheng He.

Additional information

Communicated by Masao Fukushima and Liqun Qi.

This author was supported by NSFC Grant 10571083, the MOEC grant 20020284027 and Jiangsu NSF grant BK2002075

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He, BS., Xu, Y. & Yuan, XM. A Logarithmic-Quadratic Proximal Prediction-Correction Method for Structured Monotone Variational Inequalities. Comput Optim Applic 35, 19–46 (2006). https://doi.org/10.1007/s10589-006-6442-4

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  • DOI: https://doi.org/10.1007/s10589-006-6442-4

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