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ShanghaiTech University Knowledge Management System
Anderson acceleration for iteratively reweighted ℓ1 algorithm | |
2024-03-12 | |
状态 | 已发表 |
摘要 | Iteratively reweighted L1 (IRL1) algorithm is a common algorithm for solving sparse optimization problems with nonconvex and nonsmooth regularization. The development of its acceleration algorithm, often employing Nesterov acceleration, has sparked significant interest. Nevertheless, the convergence and complexity analysis of these acceleration algorithms consistently poses substantial challenges. Recently, Anderson acceleration has gained prominence owing to its exceptional performance for speeding up fixed-point iteration, with numerous recent studies applying it to gradient -based algorithms. Motivated by the powerful impact of Anderson acceleration, we propose an Anderson -accelerated IRL1 algorithm and establish its local linear convergence rate. We extend this convergence result, typically observed in smooth settings, to a nonsmooth scenario. Importantly, our theoretical results do not depend on the Kurdyka- Lojasiewicz condition, a necessary condition in existing Nesterov acceleration -based algorithms. Furthermore, to ensure global convergence, we introduce a globally convergent Anderson accelerated IRL1 algorithm by incorporating a classical nonmonotone line search condition. Experimental results indicate that our algorithm outperforms existing Nesterov acceleration -based algorithms. |
关键词 | Anderson acceleration Iteratively reweighted ℓ1 algorithm Sparse optimization Nonconvex regularization Fixed-point iteration |
DOI | arXiv:2403.07271 |
相关网址 | 查看原文 |
出处 | Arxiv |
WOS记录号 | PPRN:88120281 |
WOS类目 | Computer Science, Artificial Intelligence ; Engineering, Electrical& Electronic ; Mathematics |
文献类型 | 预印本 |
条目标识符 | https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/372971 |
专题 | 信息科学与技术学院 信息科学与技术学院_硕士生 |
通讯作者 | Li, Kexin |
作者单位 | ShanghaiTech Univ, Sch Informat Sci & Technol, Shanghai, Peoples R China |
推荐引用方式 GB/T 7714 | Li, Kexin. Anderson acceleration for iteratively reweighted ℓ1 algorithm. 2024. |
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