Document Type : Research Paper

Authors

• Abdellah Bnouhachem ¹
• Th.M. Rassias ²

¹ Ibn Zohr University, ENSA, BP 1136, Agadir, Morocco

² Department of Mathematics, National Technical University of Athens, Zofrafou Campus, 15780 Athens, Greece

Abstract

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.

Keywords

• Variational inequalities
• monotone operator
• square quadratic proximal method
• logarithmic-quadratic proximal method
• alternating direction method