In this paper, we propose an inexact alternating direction method with square quadratic proximal (SQP) regularization for the structured variational inequalities. The predictor is obtained via solving SQP system approximately under significantly relaxed accuracy criterion and the new iterate is computed directly by an explicit formula derived from the original SQP method. Under appropriate conditions, the global convergence of the proposed method is proved. We show the $O(1/t)$ convergence rate for the inexact SQP alternating direction method. We also reported some numerical results to illustrate the efficiency of the proposed method.
Bnouhachem, A. & Rassias, T. (2017). An inexact alternating direction method with SQP regularization for the structured variational inequalities. International Journal of Nonlinear Analysis and Applications, 8(1), 269–289. https://doi.org/10.22075/ijnaa.2017.1860.1485
MLA
Bnouhachem, A., & Rassias, T. "An inexact alternating direction method with SQP regularization for the structured variational inequalities", International Journal of Nonlinear Analysis and Applications, 8, 1, 2017, 269–289. doi: 10.22075/ijnaa.2017.1860.1485
HARVARD
Bnouhachem, A., & Rassias, T. (2017). 'An inexact alternating direction method with SQP regularization for the structured variational inequalities', International Journal of Nonlinear Analysis and Applications, 8(1), pp. 269–289. doi: 10.22075/ijnaa.2017.1860.1485
CHICAGO
Bnouhachem, A. & Rassias, T., "An inexact alternating direction method with SQP regularization for the structured variational inequalities." International Journal of Nonlinear Analysis and Applications, 8 1 (2017): 269–289, doi: 10.22075/ijnaa.2017.1860.1485
VANCOUVER
Bnouhachem A., Rassias T. An inexact alternating direction method with SQP regularization for the structured variational inequalities. IJNAA. 2017;8(1):269–289. doi: 10.22075/ijnaa.2017.1860.1485
International Journal of Nonlinear Analysis and Applications