An LQP-SQP alternating direction method for solving variational inequality problems with separable structure


Authors

Adnan Alhomaidan - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. Abdellah Bnouhachem - Laboratoire d'Ingénierie des Systèmes et Technologies de l'Information, Ibn Zohr University, Agadir, BP 1136, Morocco. Abdul Latif - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.


Abstract

In this paper, by combining the logarithmic-quadratic proximal (LQP) method and the square quadratic proximal (SQP) method, we propose an inexact alternating direction method for solving constrained variational inequalities \(VI(S,f),\) where \(S\) is a convex set with linear constraints. Under certain conditions, the global convergence of the proposed method is established. We show the O(1/t) convergence rate for the inexact LQP-SQP alternating direction method. To demonstrate the efficiency of the proposed method, we provide numerical results for traffic equilibrium problems.


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ISRP Style

Adnan Alhomaidan, Abdellah Bnouhachem, Abdul Latif, An LQP-SQP alternating direction method for solving variational inequality problems with separable structure, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 12, 6246--6261

AMA Style

Alhomaidan Adnan, Bnouhachem Abdellah, Latif Abdul, An LQP-SQP alternating direction method for solving variational inequality problems with separable structure. J. Nonlinear Sci. Appl. (2017); 10(12):6246--6261

Chicago/Turabian Style

Alhomaidan, Adnan, Bnouhachem, Abdellah, Latif, Abdul. "An LQP-SQP alternating direction method for solving variational inequality problems with separable structure." Journal of Nonlinear Sciences and Applications, 10, no. 12 (2017): 6246--6261


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