A Note on the Alternating Direction Method of Multipliers

We consider the linearly constrained separable convex programming, whose objective function is separable into m individual convex functions without coupled variables. The alternating direction method of multipliers has been well studied in the literature for the special case m =2, while it remains o...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 155; no. 1; pp. 227 - 238
Main Authors: Han, Deren, Yuan, Xiaoming
Format: Journal Article
Language:English
Published: Boston Springer US 01.10.2012
Springer Nature B.V
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Constraints
Convergence
Convex analysis
Engineering
Lagrange multiplier
Mathematical functions
Mathematics
Mathematics and Statistics
Multipliers
Operations Research/Decision Theory
Optimization
Programming
Studies
Theory of Computation
Alternating direction method of multipliers
Strongly convex functions
Global convergence
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:We consider the linearly constrained separable convex programming, whose objective function is separable into m individual convex functions without coupled variables. The alternating direction method of multipliers has been well studied in the literature for the special case m =2, while it remains open whether its convergence can be extended to the general case m ≥3. This note shows the global convergence of this extension when the involved functions are further assumed to be strongly convex.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-012-0003-z