# On alternating direction method for solving variational inequality problems with separable structure

Volume 10, Issue 1, pp 175--185 Publication Date: January 27, 2017       Article History
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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.

### Keywords

• Variational inequalities
• monotone operator
• projection method
• alternating direction method.

•  49J40
•  65N30

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