A Remark on the Convergence of the Douglas–Rachford Iteration in a Non-convex Setting

被引：0
|
作者：
Ohad Giladi
机构：
[1] University of Newcastle,School of Mathematical and Physical Sciences
来源：
Set-Valued and Variational Analysis | 2018年 / 26卷
关键词：
Douglas–Rachford iteration; Lyapunov function; -stability; 49N60; 47J25; 39A22;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Using a known construction of a Lyapunov function, it is shown that the Douglas–Rachford iteration with respect to a sphere and a line in a Hilbert space converges to the intersection point in a fashion which is stronger than uniform convergence on compact sets.
引用
收藏
页码：207 / 225
页数：18
相关论文
共 50 条
  • [31] On the convergence rate of Douglas–Rachford operator splitting method
    Bingsheng He
    Xiaoming Yuan
    Mathematical Programming, 2015, 153 : 715 - 722
  • [32] On non-ergodic convergence rate of Douglas–Rachford alternating direction method of multipliers
    Bingsheng He
    Xiaoming Yuan
    Numerische Mathematik, 2015, 130 : 567 - 577
  • [33] Nesting of non-convex figures in non-convex contours
    Vinade, C.
    Dias, A.
    Informacion Tecnologica, 2000, 11 (01): : 149 - 156
  • [34] Γ-convergence of non-local, non-convex functionals in one dimension
    Brezis, Haim
    Hoai-Minh Nguyen
    COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2020, 22 (07)
  • [35] The Douglas-Rachford algorithm in the affine-convex case
    Bauschke, Heinz H.
    Dao, Minh N.
    Moursi, Walaa M.
    OPERATIONS RESEARCH LETTERS, 2016, 44 (03) : 379 - 382
  • [36] Douglas-Rachford splitting and ADMM for pathological convex optimization
    Ryu, Ernest K.
    Liu, Yanli
    Yin, Wotao
    COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2019, 74 (03) : 747 - 778
  • [37] On Slater’s condition and finite convergence of the Douglas–Rachford algorithm for solving convex feasibility problems in Euclidean spaces
    Heinz H. Bauschke
    Minh N. Dao
    Dominikus Noll
    Hung M. Phan
    Journal of Global Optimization, 2016, 65 : 329 - 349
  • [38] LEARNABLE DOUGLAS-RACHFORD ITERATION AND ITS APPLICATIONS IN DOT IMAGING
    Liu, Jiulong
    Chen, Nanguang
    Ji, Hui
    INVERSE PROBLEMS AND IMAGING, 2020, 14 (04) : 683 - 700
  • [39] The Douglas-Rachford algorithm for convex and nonconvex feasibility problems
    Aragon Artacho, Francisco J.
    Campoy, Ruben
    Tam, Matthew K.
    MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 2020, 91 (02) : 201 - 240
  • [40] Conditions for linear convergence of the gradient method for non-convex optimization
    Abbaszadehpeivasti, Hadi
    de Klerk, Etienne
    Zamani, Moslem
    OPTIMIZATION LETTERS, 2023, 17 (05) : 1105 - 1125
12345