scholarly journals A Parallel Splitting Method for Coupled Monotone Inclusions

2010 ◽  
Vol 48 (5) ◽  
pp. 3246-3270 ◽  
Author(s):  
Hédy Attouch ◽  
Luis M. Briceño-Arias ◽  
Patrick L. Combettes
Keyword(s):  
Splitting Method ◽  
Monotone Inclusions ◽  
Parallel Splitting

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 note on augmented Lagrangian-based parallel splitting method

2014 ◽  
Vol 9 (6) ◽  
pp. 1199-1212 ◽  
Author(s):  
Kai Wang ◽  
Jitamitra Desai ◽  
Hongjin He
Keyword(s):  
Augmented Lagrangian ◽  
Splitting Method ◽  
Parallel Splitting

scholarly journals A Forward-Backward Splitting Method for Monotone Inclusions Without Cocoercivity

2020 ◽  
Vol 30 (2) ◽  
pp. 1451-1472 ◽  
Author(s):  
Yura Malitsky ◽  
Matthew K. Tam
Keyword(s):  
Splitting Method ◽  
Monotone Inclusions
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