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Volume 21, Issue 4
A Modified Variable-Penalty Alternating Directions Method for Monotone Variational Inequalities

Bing-Sheng He, Sheng-Li Wang & Hai Yang

J. Comp. Math., 21 (2003), pp. 495-504.

Published online: 2003-08

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  • Abstract

Alternating directions method is one of the approaches for solving linearly constrained separate monotone variational inequalities. Experience on applications has shown that the number of iteration significantly depends on the penalty for the system of linearly constrained equations and therefore the method with variable penalties is advantageous in practice. In this paper, we extend the Kontogiorgis and Meyer method [12] by removing the monotonicity assumption on the variable penalty matrices. Moreover, we introduce a self-adaptive rule that leads the method to be more efficient and insensitive for various initial penalties. Numerical results for a class of Fermat-Weber problems show that the modified method and its self-adaptive technique are proper and necessary in practice.

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@Article{JCM-21-495, author = {He , Bing-ShengWang , Sheng-Li and Yang , Hai}, title = {A Modified Variable-Penalty Alternating Directions Method for Monotone Variational Inequalities}, journal = {Journal of Computational Mathematics}, year = {2003}, volume = {21}, number = {4}, pages = {495--504}, abstract = {

Alternating directions method is one of the approaches for solving linearly constrained separate monotone variational inequalities. Experience on applications has shown that the number of iteration significantly depends on the penalty for the system of linearly constrained equations and therefore the method with variable penalties is advantageous in practice. In this paper, we extend the Kontogiorgis and Meyer method [12] by removing the monotonicity assumption on the variable penalty matrices. Moreover, we introduce a self-adaptive rule that leads the method to be more efficient and insensitive for various initial penalties. Numerical results for a class of Fermat-Weber problems show that the modified method and its self-adaptive technique are proper and necessary in practice.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10253.html} }
TY - JOUR T1 - A Modified Variable-Penalty Alternating Directions Method for Monotone Variational Inequalities AU - He , Bing-Sheng AU - Wang , Sheng-Li AU - Yang , Hai JO - Journal of Computational Mathematics VL - 4 SP - 495 EP - 504 PY - 2003 DA - 2003/08 SN - 21 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10253.html KW - Monotone variational inequalities, Alternating directions method, Fermat-Weber problem. AB -

Alternating directions method is one of the approaches for solving linearly constrained separate monotone variational inequalities. Experience on applications has shown that the number of iteration significantly depends on the penalty for the system of linearly constrained equations and therefore the method with variable penalties is advantageous in practice. In this paper, we extend the Kontogiorgis and Meyer method [12] by removing the monotonicity assumption on the variable penalty matrices. Moreover, we introduce a self-adaptive rule that leads the method to be more efficient and insensitive for various initial penalties. Numerical results for a class of Fermat-Weber problems show that the modified method and its self-adaptive technique are proper and necessary in practice.

Bing-Sheng He, Sheng-Li Wang & Hai Yang. (1970). A Modified Variable-Penalty Alternating Directions Method for Monotone Variational Inequalities. Journal of Computational Mathematics. 21 (4). 495-504. doi:
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