On alternating direction method for solving variational inequality problems with separable structure
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Authors
Abdellah Bnouhachem
- Laboratoire d’Ingénierie des Systémes et Technologies de l’Information, ENSA, Ibn Zohr University, Agadir, BP 1136, Morocco.
Fatimazahra Benssi
- Laboratoire d’Ingénierie des Systémes et Technologies de l’Information, ENSA, Ibn Zohr University, Agadir, BP 1136, Morocco.
Abdelouahed Hamdi
- Department of Mathematics, Statistics and Physics College of Arts and Sciences, Qatar University, P. O. Box 2713, Doha, Qatar.
Abstract
We present an alternating direction scheme for the separable constrained convex programming problem. The predictor
is obtained via solving two sub-variational inequalities in a parallel wise at each iteration. The new iterate is obtained by a
projection type method along a new descent direction. The new direction is obtained by combining the descent directions using
by He [B.-S. He, Comput. Optim. Appl., 42 (2009), 195–212] and Jiang and Yuan [Z.-K. Jiang, X.-M. Yuan, J. Optim. Theory
Appl., 145 (2010), 311–323]. Global convergence of the proposed method is proved under certain assumptions. We also report
some numerical results to illustrate the efficiency of the proposed method.
Share and Cite
ISRP Style
Abdellah Bnouhachem, Fatimazahra Benssi, Abdelouahed Hamdi, On alternating direction method for solving variational inequality problems with separable structure, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 1, 175--185
AMA Style
Bnouhachem Abdellah, Benssi Fatimazahra, Hamdi Abdelouahed, On alternating direction method for solving variational inequality problems with separable structure. J. Nonlinear Sci. Appl. (2017); 10(1):175--185
Chicago/Turabian Style
Bnouhachem, Abdellah, Benssi, Fatimazahra, Hamdi, Abdelouahed. "On alternating direction method for solving variational inequality problems with separable structure." Journal of Nonlinear Sciences and Applications, 10, no. 1 (2017): 175--185
Keywords
- Variational inequalities
- monotone operator
- projection method
- alternating direction method.
MSC
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