Geodesic
An LQP-SQP alternating direction method for solving variational inequality problems with separable structure
Alhomaidan, Adnan 1 ; Bnouhachem, Abdellah 2 ; Latif, Abdul 1
1 Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
2 Laboratoire d'Ingénierie des Systèmes et Technologies de l'Information, Ibn Zohr University, Agadir, BP 1136, Morocco
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 12, p. 6246-6261.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.010.12.10
Classification : 90C33, 49J405
Keywords: Proximal point algorithm, logarithmic-quadratic proximal method, square quadratic proximal, variational inequality, prediction-correction, traffic equilibrium problems

Alhomaidan, Adnan  1 ; Bnouhachem, Abdellah  2 ; Latif, Abdul  1

1 Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
2 Laboratoire d'Ingénierie des Systèmes et Technologies de l'Information, Ibn Zohr University, Agadir, BP 1136, Morocco 
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     title = {An {LQP-SQP} alternating direction method for solving variational inequality problems with separable structure},
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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 its applications, Tome 10 (2017) no. 12, p. 6246-6261. doi : 10.22436/jnsa.010.12.10. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.12.10/

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