scholarly journals Convergence Analysis of Alternating Direction Method of Multipliers for a Family of Nonconvex Problems

2016 ◽  
Vol 26 (1) ◽  
pp. 337-364 ◽  
Author(s):  
Mingyi Hong ◽  
Zhi-Quan Luo ◽  
Meisam Razaviyayn
Keyword(s):  
Convergence Analysis ◽  
Alternating Direction Method ◽  
Method Of Multipliers ◽  
Nonconvex Problems ◽  
Alternating Direction

scholarly journals Convergence Analysis of Alternating Direction Method of Multipliers for a Class of Separable Convex Programming

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Zehui Jia ◽  
Ke Guo ◽  
Xingju Cai
Keyword(s):  
Convergence Analysis ◽  
Convex Programming ◽  
Alternating Direction Method ◽  
Linear Functions ◽  
Method Of Multipliers ◽  
Strongly Convex Functions ◽  
Strongly Convex ◽  
Alternating Direction ◽  
Separable Convex Programming ◽  
The Individual

The purpose of this paper is extending the convergence analysis of Han and Yuan (2012) for alternating direction method of multipliers (ADMM) from the strongly convex to a more general case. Under the assumption that the individual functions are composites of strongly convex functions and linear functions, we prove that the classical ADMM for separable convex programming with two blocks can be extended to the case with more than three blocks. The problems, although still very special, arise naturally from some important applications, for example, route-based traffic assignment problems.

scholarly journals A Survey on Some Recent Developments of Alternating Direction Method of Multipliers

2022 ◽  
Author(s):  
De-Ren Han
Keyword(s):  
Rate Of Convergence ◽  
Alternating Direction Method ◽  
Theoretical Studies ◽  
Method Of Multipliers ◽  
Nonconvex Problems ◽  
Alternating Direction ◽  
Recent Developments

AbstractRecently, alternating direction method of multipliers (ADMM) attracts much attentions from various fields and there are many variant versions tailored for different models. Moreover, its theoretical studies such as rate of convergence and extensions to nonconvex problems also achieve much progress. In this paper, we give a survey on some recent developments of ADMM and its variants.

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