Name
Abstract | ||
|---|---|---|
We provide a simple analysis of the Douglas-Rachford splitting algorithm in the context of l(1) minimization with linear constraints, and quantify the asymptotic linear convergence rate in terms of principal angles between relevant vector spaces. In the compressed sensing setting, we show how to bound this rate in terms of the restricted isometry constant. More general iterative schemes obtained by l(2)-regularization and over-relaxation including the dual split Bregman method are also treated, which answers the question of how to choose the relaxation and soft-thresholding parameters to accelerate the asymptotic convergence rate. We make no attempt at characterizing the transient regime preceding the onset of linear convergence. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1090/mcom/2965 | MATHEMATICS OF COMPUTATION |
Keywords | Field | DocType |
Basis pursuit,Douglas-Rachford,generalized Douglas-Rachford,Peaceman-Rachford,relaxation parameter,asymptotic linear convergence rate | Mathematical optimization,Vector space,Principal angles,Mathematical analysis,Isometry,Basis pursuit,Minification,Bregman method,Rate of convergence,Mathematics,Compressed sensing | Journal |
Volume | Issue | ISSN |
85 | 297 | 0025-5718 |
Citations | PageRank | References |
5 | 0.47 | 15 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Laurent Demanet | 1 | 750 | 57.81 |
| Xiangxiong Zhang | 2 | 462 | 32.93 |