An accelerated augmented Lagrangian method for linearly constrained convex programming with the rate of convergence O(1/k2)

In this paper, we propose and analyze an accelerated augmented Lagrangian method (denoted by AALM) for solving the linearly constrained convex programming. We show that the convergence rate of AALM is O (1/ k 2 ) while the convergence rate of the classical augmented Lagrangian method (ALM) is O (1/...

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Veröffentlicht in:Applied Mathematics-A Journal of Chinese Universities Jg. 32; H. 1; S. 117 - 126
Hauptverfasser: Ke, Yi-fen, Ma, Chang-feng
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Hangzhou Editorial Committee of Applied Mathematics - A Journal of Chinese Universities 01.03.2017
Springer Nature B.V
Schlagworte:
Applications of Mathematics
Convergence
Convexity
Lagrange multiplier
Mathematics
Mathematics and Statistics
Nonlinear programming
convex programming
augmented Lagrangian method
accelerated technique
linearly constrained
ISSN:1005-1031, 1993-0445
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Zusammenfassung:In this paper, we propose and analyze an accelerated augmented Lagrangian method (denoted by AALM) for solving the linearly constrained convex programming. We show that the convergence rate of AALM is O (1/ k 2 ) while the convergence rate of the classical augmented Lagrangian method (ALM) is O (1/ k ). Numerical experiments on the linearly constrained l 1 − l 2 minimization problem are presented to demonstrate the effectiveness of AALM.
Bibliographie:ObjectType-Article-1
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ISSN:1005-1031
1993-0445
DOI:10.1007/s11766-017-3381-z