Name
Title | ||
|---|---|---|
Alternating Direction Method of Multipliers for a Class of Nonconvex and Nonsmooth Problems with Applications to Background/Foreground Extraction. |
Abstract | ||
|---|---|---|
In this paper, we study a general optimization model, which covers a large class of existing models for many applications in imaging sciences. To solve the resulting possibly nonconvex, nonsmooth and non-Lipschitz optimization problem, we adapt the alternating direction method of multipliers (ADMM) with a general dual step-size to solve a reformulation that contains three blocks of variables, and analyze its convergence. We show that for any dual step-size less than the golden ratio, there exists a computable threshold such that if the penalty parameter is chosen above such a threshold and the sequence thus generated by our ADMM is bounded, then the cluster point of the sequence gives a stationary point of the nonconvex optimization problem. We achieve this via apotential function specifically constructed for our ADMM. Moreover, we establish the global conver-gence of the whole sequence if, in addition, this special pot ential function is a Kurdyka-Lojasiewicz function. Furthermore, we present a simple strategy for initializing the algorithm to guarantee bound-edness of the sequence. Finally, we perform numerical experiments comparing our ADMM with the proximal alternating linearized minimization (PALM) proposed in [5] on the background/foreground extraction problem with real data. The numerical results show that our ADMM with a nontrivial dual step-size is efficient. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1137/15M1027528 | SIAM JOURNAL ON IMAGING SCIENCES |
Keywords | Field | DocType |
nonsmooth and nonconex optimization,alternating dirtection method of multipliers,dual step-size,background/foreground extraction | Convergence (routing),Mathematical optimization,Existential quantification,Golden ratio,Stationary point,Minification,Initialization,Optimization problem,Mathematics,Bounded function | Journal |
Volume | Issue | ISSN |
10 | 1 | 1936-4954 |
Citations | PageRank | References |
21 | 0.64 | 30 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Lei Yang | 1 | 43 | 3.05 |
| Ting Kei Pong | 2 | 427 | 23.18 |
| Xiaojun Chen | 3 | 1298 | 107.51 |