LOCAL LINEAR CONVERGENCE OF THE ALTERNATING DIRECTION METHOD OF MULTIPLIERS FOR QUADRATIC PROGRAMS

被引：93
|
作者：
Han, Deren [1 ]
Yuan, Xiaoming [2 ]
机构：
[1] Nanjing Normal Univ, Sch Math Sci, Key Lab NSLSCS Jiangsu Prov, Nanjing 210046, Jiangsu, Peoples R China
[2] Hong Kong Baptist Univ, Inst Computat & Theoret Studies, Dept Math, Hong Kong, Hong Kong, Peoples R China
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2013年 / 51卷 / 06期
关键词：
alternating direction method of multipliers; linear convergence rate; quadratic program; error bound; SPLITTING ALGORITHMS;
D O I：
10.1137/120886753
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The Douglas-Rachford alternating direction method of multipliers (ADMM) has been widely used in various areas. The global convergence of ADMM is well known, while research on its convergence rate is still in its infancy. In this paper, we show the local linear convergence rate of ADMM for a quadratic program which includes some important applications of ADMM as special cases.
引用
收藏
页码：3446 / 3457
页数：12
相关论文
共 50 条
  • [41] Optimal Parameter Selection for the Alternating Direction Method of Multipliers (ADMM): Quadratic Problems
    Ghadimi, Euhanna
    Teixeira, Andre
    Shames, Iman
    Johansson, Mikael
    IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2015, 60 (03) : 644 - 658
  • [42] An alternating direction method of multipliers with the BFGS update for structured convex quadratic optimization
    Gu, Yan
    Yamashita, Nobuo
    COMPUTATIONAL & APPLIED MATHEMATICS, 2021, 40 (03):
  • [43] GLOBAL LINEAR CONVERGENCE RATE OF THE LINEARIZED VERSION OF THE GENERALIZED ALTERNATING DIRECTION METHOD OF MULTIPLIERS FOR SEPARABLE CONVEX PROGRAMMING
    Peng, Jianwen
    Zhang, Xueqing
    Yao, Jen-Chih
    Liu, Dexi
    JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2024, 25 (02) : 355 - 371
  • [44] The convergence rate of the proximal alternating direction method of multipliers with indefinite proximal regularization
    Min Sun
    Jing Liu
    Journal of Inequalities and Applications, 2017
  • [45] The exact worst-case convergence rate of the alternating direction method of multipliers
    Zamani, Moslem
    Abbaszadehpeivasti, Hadi
    de Klerk, Etienne
    MATHEMATICAL PROGRAMMING, 2024, 208 (1-2) : 243 - 276
  • [46] The Proximal Alternating Direction Method of Multipliers in the Nonconvex Setting: Convergence Analysis and Rates
    Bot, Radu Ioan
    Dang-Khoa Nguyen
    MATHEMATICS OF OPERATIONS RESEARCH, 2020, 45 (02) : 682 - 712
  • [47] An Inertial Alternating Direction Method of Multipliers
    Bot, Radu Ioan
    Csetnek, Ernoe Robert
    MINIMAX THEORY AND ITS APPLICATIONS, 2016, 1 (01): : 29 - 49
  • [48] Parallel alternating direction method of multipliers
    Yan, Jiaqi
    Guo, Fanghong
    Wen, Changyun
    Li, Guoqi
    INFORMATION SCIENCES, 2020, 507 : 185 - 196
  • [49] On the O (1/k) Convergence of Asynchronous Distributed Alternating Direction Method of Multipliers
    Wei, Ermin
    Ozdaglar, Asuman
    2013 IEEE GLOBAL CONFERENCE ON SIGNAL AND INFORMATION PROCESSING (GLOBALSIP), 2013, : 551 - 554
  • [50] A fundamental proof of convergence of alternating direction method of multipliers for weakly convex optimization
    Zhang, Tao
    Shen, Zhengwei
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2019, 2019 (1)
12345