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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
DOIarXiv:2403.07271
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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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