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http://hdl.handle.net/10397/68369
| Title: | Alternating direction method of multipliers for a class of nonconvex and nonsmooth problems with applications to background/foreground extraction | Authors: | Yang, L Pong, TK Chen, X |
Issue Date: | 2017 | Source: | SIAM journal on imaging sciences, 2017, v. 10, no. 1, p. 74-110 | 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. | Keywords: | Nonsmooth and nonconex optimization Alternating dirtection method of multipliers Dual step-size Background/foreground extraction |
Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM journal on imaging sciences | ISSN: | 1936-4954 | DOI: | 10.1137/15M1027528 | Rights: | © 2017 Society for Industrial and Applied Mathematics The following publication Yang, L., Pong, T. K., & Chen, X. (2017). Alternating direction method of multipliers for a class of nonconvex and nonsmooth problems with applications to background/foreground extraction. SIAM Journal on Imaging Sciences, 10(1), 74-110 is available at https://doi.org/10.1137/15M1027528 |
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| 15m1027528.pdf | 1.26 MB | Adobe PDF | View/Open |
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