On the global and linear convergence of direct extension of ADMM for 3-block separable convex minimization models

In this paper, we show that when the alternating direction method of multipliers (ADMM) is extended directly to the 3-block separable convex minimization problems, it is convergent if one block in the objective possesses sub-strong monotonicity which is weaker than strong convexity. In particular, w...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2016; no. 1; pp. 1 - 14
Main Authors Sun, Huijie, Wang, Jinjiang, Deng, Tingquan
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 17.09.2016
Springer Nature B.V
SpringerOpen
Subjects
alternating direction method of multiplier
Analysis
Applications of Mathematics
Complexity
Convergence
Estimates
Inequalities
Iterative methods
Karush-Kuhn-Tucher (KKT) system
linear convergence rate
Mathematics
Mathematics and Statistics
Minimization
Multipliers
Optimization
separable convex optimization
strong monotonicity
separable convex optimization
Karush-Kuhn-Tucher (KKT) system
strong monotonicity
alternating direction method of multiplier
linear convergence rate
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Summary:In this paper, we show that when the alternating direction method of multipliers (ADMM) is extended directly to the 3-block separable convex minimization problems, it is convergent if one block in the objective possesses sub-strong monotonicity which is weaker than strong convexity. In particular, we estimate the globally linear convergence rate of the direct extension of ADMM measured by the iteration complexity under some additional conditions.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-016-1173-2