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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Bibliographic Details
Published in:Applied Mathematics-A Journal of Chinese Universities Vol. 32; no. 1; pp. 117 - 126
Main Authors: Ke, Yi-fen, Ma, Chang-feng
Format: Journal Article
Language:English
Published: Hangzhou Editorial Committee of Applied Mathematics - A Journal of Chinese Universities 01.03.2017
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:1005-1031
1993-0445
DOI:10.1007/s11766-017-3381-z