A parallel splitting ALM-based algorithm for separable convex programming

2021 ◽  
Author(s):  
Shengjie Xu ◽  
Bingsheng He
Keyword(s):  
Convex Programming ◽  
Separable Convex Programming ◽  
Parallel Splitting

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

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Jing Liu ◽  
Yongrui Duan ◽  
Tonghui Wang
Keyword(s):  
Convex Programming ◽  
Augmented Lagrangian ◽  
Augmented Lagrangian Method ◽  
Lagrangian Method ◽  
Step Size ◽  
Linear Equality Constraints ◽  
Separable Convex Programming ◽  
Parallel Splitting ◽  
Separable Convex Minimization ◽  
Alm Method

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.

scholarly journals A Proximal Fully Parallel Splitting Method for Stable Principal Component Pursuit

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Hongchun Sun ◽  
Jing Liu ◽  
Min Sun
Keyword(s):  
Signal Processing ◽  
Statistical Learning ◽  
Splitting Method ◽  
Principal Component ◽  
Computational Results ◽  
Closed Form Solutions ◽  
Mild Conditions ◽  
Separable Convex Programming ◽  
Parallel Splitting ◽  
Principal Component Pursuit

As a special three-block separable convex programming, the stable principal component pursuit (SPCP) arises in many different disciplines, such as statistical learning, signal processing, and web data ranking. In this paper, we propose a proximal fully parallel splitting method (PFPSM) for solving SPCP, in which the resulting subproblems all admit closed-form solutions and can be solved in distributed manners. Compared with other similar algorithms in the literature, PFPSM attaches a Glowinski relaxation factor η∈3/2,2/3 to the updating formula for its Lagrange multiplier, which can be used to accelerate the convergence of the generated sequence. Under mild conditions, the global convergence of PFPSM is proved. Preliminary computational results show that the proposed algorithm works very well in practice.

A splitting method for separable convex programming

2014 ◽  
Vol 35 (1) ◽  
pp. 394-426 ◽  
Author(s):  
B. He ◽  
M. Tao ◽  
X. Yuan
Keyword(s):  
Convex Programming ◽  
Splitting Method ◽  
Separable Convex Programming
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