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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of optimization theory and applications Jg. 155; H. 1; S. 227 - 238
Hauptverfasser: Han, Deren, Yuan, Xiaoming
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Boston Springer US 01.10.2012
Springer Nature B.V
Schlagworte:
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-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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.
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ObjectType-Article-2
content type line 23
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-012-0003-z