Convergence rate analysis of proximal iteratively reweighted l1 methods for lp regularization problems

被引：0
|
作者：
Wang, Hao [1 ]
Zeng, Hao [1 ]
Wang, Jiashan [2 ]
机构：
[1] ShanghaiTech Univ, Sch Informat Sci & Technol, Shanghai, Peoples R China
[2] Univ Washington, Dept Math, Seattle, WA 98195 USA
来源：
OPTIMIZATION LETTERS | 2023年 / 17卷 / 02期
基金：
上海市自然科学基金; 中国国家自然科学基金;
关键词：
Kurdyka-Lojasiewicz property; Iteratively reweighted algorithm; l(p) regularization; Convergence rate; MINIMIZATION; ALGORITHM; NONCONVEX; SPARSITY;
D O I：
10.1007/s11590-022-01907-4
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：
In this paper, we focus on the local convergence rate analysis of the proximal iteratively reweighted l(1) algorithms for solving l(p) regularization problems, which are widely applied for inducing sparse solutions. We show that if the KurdykaLojasiewicz property is satisfied, the algorithm converges to a unique first-order stationary point; furthermore, the algorithm has local linear convergence or local sublinear convergence. The theoretical results we derived are much stronger than the existing results for iteratively reweighted l(1) algorithms.
引用
收藏
页码：413 / 435
页数：23
相关论文
共 50 条
  • [41] Several accelerated subspace minimization conjugate gradient methods based on regularization model and convergence rate analysis for nonconvex problems
    Wumei Sun
    Hongwei Liu
    Zexian Liu
    Numerical Algorithms, 2022, 91 : 1677 - 1719
  • [42] COMBINED LP AND QUASI-NEWTON METHODS FOR NONLINEAR L1 OPTIMIZATION
    HALD, J
    MADSEN, K
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 1985, 22 (01) : 68 - 80
  • [43] Several accelerated subspace minimization conjugate gradient methods based on regularization model and convergence rate analysis for nonconvex problems
    Sun, Wumei
    Liu, Hongwei
    Liu, Zexian
    NUMERICAL ALGORITHMS, 2022, 91 (04) : 1677 - 1719
  • [44] STRONG-CONVERGENCE IN L1 IMPLIED BY WEAK - TRUNCATION METHODS
    AMRANI, A
    CASTAING, C
    VALADIER, M
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1992, 314 (01): : 37 - 40
  • [45] RIP Analysis for l1/lp (p > 1) Minimization Method
    Xie, Yujia
    Su, Xinhua
    Ge, Huanmin
    IEEE SIGNAL PROCESSING LETTERS, 2023, 30 : 997 - 1001
  • [46] Convergence rate analysis of domain decomposition methods for obstacle problems
    Tai, X.-C.
    East-West Journal of Numerical Mathematics, 2001, 9 (03): : 233 - 252
  • [47] Solution of l1 minimization problems by LARS/homotopy methods
    Drori, Iddo
    Donoho, David L.
    2006 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING, VOLS 1-13, 2006, : 3087 - 3090
  • [48] A variable projection method for large-scale inverse problems with l1 regularization
    Chung, Matthias
    Renaut, Rosemary A.
    APPLIED NUMERICAL MATHEMATICS, 2023, 192 : 297 - 318
  • [49] RECURRENT NEURAL NETWORK WITH L1/2 REGULARIZATION FOR REGRESSION AND MULTICLASS CLASSIFICATION PROBLEMS
    Li, Lin
    Fan, Qinwei
    Zhou, Li
    JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS, 2022, 2022
  • [50] RECURRENT NEURAL NETWORK WITH L1/2 REGULARIZATION FOR REGRESSION AND MULTICLASS CLASSIFICATION PROBLEMS
    Li, Lin
    Fan, Qinwei
    Zhou, Li
    JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS, 2022, 2022
12345