Convergence of the reweighted l1 minimization algorithm for l2-lp minimization

被引：76
|
作者：
Chen, Xiaojun [1 ]
Zhou, Weijun [2 ]
机构：
[1] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China
[2] Changsha Univ Sci & Technol, Dept Math, Changsha 410004, Hunan, Peoples R China
来源：
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS | 2014年 / 59卷 / 1-2期
关键词：
l(p) minimization; Stationary points; Nonsmooth and nonconvex optimization; Pseudo convex; Global convergence; RECONSTRUCTION; NONSMOOTH; SIGNALS; IMAGES;
D O I：
10.1007/s10589-013-9553-8
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
The iteratively reweighted a"" (1) minimization algorithm (IRL1) has been widely used for variable selection, signal reconstruction and image processing. In this paper, we show that any sequence generated by the IRL1 is bounded and any accumulation point is a stationary point of the a"" (2)-a"" (p) minimization problem with 0 < p < 1. Moreover, the stationary point is a global minimizer and the convergence rate is approximately linear under certain conditions. We derive posteriori error bounds which can be used to construct practical stopping rules for the algorithm.
引用
收藏
页码：47 / 61
页数：15
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