Volume 27, Issue 4
A Comparison of Different Contraction Methods for Monotone Variational Inequalities

J. Comp. Math., 27 (2009), pp. 459-473.

Published online: 2009-08

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• Abstract

It is interesting to compare the efficiency of two methods when their computational loads in each iteration are equal. In this paper, two classes of contraction methods for monotone variational inequalities are studied in a unified framework. The methods of both classes can be viewed as prediction-correction methods, which generate the same test vector in the prediction step and adopt the same step-size rule in the correction step. The only difference is that they use different search directions. The computational loads of each iteration of the different classes are equal. Our analysis explains theoretically why one class of the contraction methods usually outperforms the other class. It is demonstrated that many known methods belong to these two classes of methods. Finally, the presented numerical results demonstrate the validity of our analysis.

• Keywords

Monotone variational inequalities, Prediction-correction, Contraction methods.

65K10, 90C25, 90C30.

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@Article{JCM-27-459, author = {}, title = {A Comparison of Different Contraction Methods for Monotone Variational Inequalities}, journal = {Journal of Computational Mathematics}, year = {2009}, volume = {27}, number = {4}, pages = {459--473}, abstract = {

It is interesting to compare the efficiency of two methods when their computational loads in each iteration are equal. In this paper, two classes of contraction methods for monotone variational inequalities are studied in a unified framework. The methods of both classes can be viewed as prediction-correction methods, which generate the same test vector in the prediction step and adopt the same step-size rule in the correction step. The only difference is that they use different search directions. The computational loads of each iteration of the different classes are equal. Our analysis explains theoretically why one class of the contraction methods usually outperforms the other class. It is demonstrated that many known methods belong to these two classes of methods. Finally, the presented numerical results demonstrate the validity of our analysis.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.27.4.013}, url = {http://global-sci.org/intro/article_detail/jcm/8583.html} }
TY - JOUR T1 - A Comparison of Different Contraction Methods for Monotone Variational Inequalities JO - Journal of Computational Mathematics VL - 4 SP - 459 EP - 473 PY - 2009 DA - 2009/08 SN - 27 DO - http://doi.org/10.4208/jcm.2009.27.4.013 UR - https://global-sci.org/intro/article_detail/jcm/8583.html KW - Monotone variational inequalities, Prediction-correction, Contraction methods. AB -

It is interesting to compare the efficiency of two methods when their computational loads in each iteration are equal. In this paper, two classes of contraction methods for monotone variational inequalities are studied in a unified framework. The methods of both classes can be viewed as prediction-correction methods, which generate the same test vector in the prediction step and adopt the same step-size rule in the correction step. The only difference is that they use different search directions. The computational loads of each iteration of the different classes are equal. Our analysis explains theoretically why one class of the contraction methods usually outperforms the other class. It is demonstrated that many known methods belong to these two classes of methods. Finally, the presented numerical results demonstrate the validity of our analysis.

Bingsheng He , Xiang Wang & Junfeng Yang. (2019). A Comparison of Different Contraction Methods for Monotone Variational Inequalities. Journal of Computational Mathematics. 27 (4). 459-473. doi:10.4208/jcm.2009.27.4.013
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