A Parallel Splitting Augmented Lagrangian Method for Two-Block Separable Convex Programming with Application in Image Processing

The augmented Lagrangian method (ALM) is one of the most successful first-order methods for convex programming with linear equality constraints. To solve the two-block separable convex minimization problem, we always use the parallel splitting ALM method. In this paper, we will show that no matter h...

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Bibliographic Details
Published in:Mathematical problems in engineering Vol. 2020; no. 2020; pp. 1 - 10
Main Authors: Liu, Jing, Wang, Tonghui, Duan, Yongrui
Format: Journal Article
Language:English
Published: Cairo, Egypt Hindawi Publishing Corporation 2020
Hindawi
John Wiley & Sons, Inc
Subjects:
Convergence
Convexity
Image processing
Mathematical problems
Nonlinear programming
Optimization
Splitting
ISSN:1024-123X, 1563-5147
Online Access:Get full text
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Summary:The augmented Lagrangian method (ALM) is one of the most successful first-order methods for convex programming with linear equality constraints. To solve the two-block separable convex minimization problem, we always use the parallel splitting ALM method. In this paper, we will show that no matter how small the step size and the penalty parameter are, the convergence of the parallel splitting ALM is not guaranteed. We propose a new convergent parallel splitting ALM (PSALM), which is the regularizing ALM’s minimization subproblem by some simple proximal terms. In application this new PSALM is used to solve video background extraction problems and our numerical results indicate that this new PSALM is efficient.
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ISSN:1024-123X
1563-5147
DOI:10.1155/2020/6872810