A new LQP alternating direction method for solving variational inequality problems with separable structure

Optimization ◽  
2016 ◽  
Vol 65 (12) ◽  
pp. 2251-2267
Author(s):  
Abdellah Bnouhachem ◽  
Abdelouahed Hamdi ◽  
M. H. Xu
Keyword(s):  
Variational Inequality ◽  
Alternating Direction Method ◽  
Variational Inequality Problems ◽  
Separable Structure ◽  
Alternating Direction

scholarly journals SQP alternating direction method with a new optimal step size for solving variational inequality problems with separable structure

2018 ◽  
Vol 12 (1) ◽  
pp. 224-243 ◽  
Author(s):  
Abdellah Bnouhachem ◽  
Themistocles Rassias
Keyword(s):  
Variational Inequality ◽  
Alternating Direction Method ◽  
Convex Programming Problem ◽  
Descent Direction ◽  
Computational Results ◽  
Step Size ◽  
Sqp Method ◽  
Separable Structure ◽  
Alternating Direction ◽  
Optimal Step Size

In this paper, we suggest and analyze a new alternating direction scheme for the separable constrained convex programming problem. The theme of this paper is twofold. First, we consider the square-quadratic proximal (SQP) method. Next, by combining the alternating direction method with SQP method, we propose a descent SQP alternating direction method by using the same descent direction as in [6] with a new step size ?k. Under appropriate conditions, the global convergence of the proposed method is proved. We show the O(1/t) convergence rate for the SQP alternating direction method. Some preliminary computational results are given to illustrate the efficiency of the proposed method.

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