On the Optimal Step-size Selection for the Alternating Direction Method of Multipliers*

2012 ◽  
Vol 45 (26) ◽  
pp. 139-144 ◽  
Author(s):  
Euhanna Ghadimi ◽  
André Teixeira ◽  
Iman Shames ◽  
Mikael Johansson
Keyword(s):  
Alternating Direction Method ◽  
Method Of Multipliers ◽  
Step Size ◽  
Size Selection ◽  
Alternating Direction ◽  
Optimal Step Size ◽  
Selection For

scholarly journals On the Convergence Analysis of the Alternating Direction Method of Multipliers with Three Blocks

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Caihua Chen ◽  
Yuan Shen ◽  
Yanfei You
Keyword(s):  
Alternating Direction Method ◽  
Method Of Multipliers ◽  
Objective Functions ◽  
Step Size ◽  
Mild Conditions ◽  
Alternating Direction ◽  
Separable Convex Programming ◽  
Optimal Step Size ◽  
Linearly Constrained ◽  
Kkt Points

We consider a class of linearly constrained separable convex programming problems whose objective functions are the sum of three convex functions without coupled variables. For those problems, Han and Yuan (2012) have shown that the sequence generated by the alternating direction method of multipliers (ADMM) with three blocks converges globally to their KKT points under some technical conditions. In this paper, a new proof of this result is found under new conditions which are much weaker than Han and Yuan’s assumptions. Moreover, in order to accelerate the ADMM with three blocks, we also propose a relaxed ADMM involving an additional computation of optimal step size and establish its global convergence under mild conditions.

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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