On self-adaptive method for general mixed variational inequalities.
Bnouhachem, Abdellah, Noor, Muhammad Aslam, Al-Shemas, Eman H. (2008)
Mathematical Problems in Engineering
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Bnouhachem, Abdellah, Noor, Muhammad Aslam, Al-Shemas, Eman H. (2008)
Mathematical Problems in Engineering
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Noor, Muhammad Aslam, Wang, Yi Ju, Xiu, Naihua (2002)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Lu, Xiwen, Xu, Hong-Kun, Yin, Ximing (2010)
Fixed Point Theory and Applications [electronic only]
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Anh, Pham Ngoc, Kim, Jong Kyu (2010)
Journal of Inequalities and Applications [electronic only]
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Shi, Chaofeng (2007)
Mathematical Problems in Engineering
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Noor, Muhammed Aslam (1991)
International Journal of Mathematics and Mathematical Sciences
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Alfredo N. Iusem, Mostafa Nasri (2010)
RAIRO - Operations Research
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We introduce augmented Lagrangian methods for solving finite dimensional variational inequality problems whose feasible sets are defined by convex inequalities, generalizing the proximal augmented Lagrangian method for constrained optimization. At each iteration, primal variables are updated by solving an unconstrained variational inequality problem, and then dual variables are updated through a closed formula. A full convergence analysis is provided, allowing for inexact solution of...
Noor, Muhammad Aslam (1996)
Journal of Applied Mathematics and Stochastic Analysis
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Lin, Yen-Cherng (2008)
Journal of Inequalities and Applications [electronic only]
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Noor, Muhammad Aslam, Akhter, Muzaffar, Noor, Khalida Inayat (2003)
International Journal of Mathematics and Mathematical Sciences
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Alexander Kaplan, Rainer Tichatschke (2010)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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In this paper we clarify that the interior proximal method developed in [6] (vol. 27 of this journal) for solving variational inequalities with monotone operators converges under essentially weaker conditions concerning the functions describing the "feasible" set as well as the operator of the variational inequality.