MONOTONE OPERATORS AND THE PROXIMAL POINT ALGORITHM IN COMPLETE CAT(0) METRIC SPACES

被引：55
|
作者：
Khatibzadeh, Hadi [1 ]
Ranjbar, Sajad [1 ,2 ]
机构：
[1] Univ Zanjan, Dept Math, POB 45195-313, Zanjan, Iran
[2] Higher Educ Ctr Eghlid, Coll Sci, Dept Math, Eghlid, Iran
来源：
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2017年 / 103卷 / 01期
关键词：
Hadamard space; monotone operator; proximal point algorithm; Delta-convergence; subdifferential; nonexpansive mapping; DELTA-CONVERGENCE;
D O I：
10.1017/S1446788716000446
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we generalize monotone operators, their resolvents and the proximal point algorithm to complete CAT(0) spaces. We study some properties of monotone operators and their resolvents. We show that the sequence generated by the inexact proximal point algorithm Delta-converges to a zero of the monotone operator in complete CAT(0) spaces. A strong convergence (convergence in metric) result is also presented. Finally, we consider two important special cases of monotone operators and we prove that they satisfy the range condition (see Section 4 for the definition), which guarantees the existence of the sequence generated by the proximal point algorithm.
引用
收藏
页码：70 / 90
页数：21
相关论文
共 50 条
  • [1] The strong convergence of a proximal point algorithm in complete CAT(0) metric spaces
    Tahernia, Mohsen
    Moradi, Sirous
    Jafari, Somaye
    [J]. HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2020, 49 (01): : 399 - 408
  • [2] W-CONVERGENCE OF THE PROXIMAL POINT ALGORITHM IN COMPLETE CAT(0) METRIC SPACES
    Ranjbar, S.
    [J]. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2017, 43 (03) : 817 - 834
  • [3] Halpern-type proximal point algorithm in complete CAT(0) metric spaces
    Heydari, Mohammad Taghi
    Ranjbar, Sajad
    [J]. ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2016, 24 (03): : 141 - 159
  • [4] A variable metric proximal point algorithm for monotone operators
    Burke, JV
    Qian, M
    [J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1999, 37 (02) : 353 - 375
  • [5] Minimization Problem of Proximal Point Algorithm in Complete CAT(0) Spaces
    Moradi, Sirous
    Tahernia, Mohsen
    [J]. FILOMAT, 2022, 36 (18) : 6289 - 6298
  • [6] The modified proximal point algorithm in CAT(0) spaces
    Cholamjiak, Prasit
    [J]. OPTIMIZATION LETTERS, 2015, 9 (07) : 1401 - 1410
  • [7] MONOTONE OPERATORS AND PROXIMAL POINT ALGORITHM
    ROCKAFELLAR, RT
    [J]. SIAM JOURNAL ON CONTROL, 1976, 14 (05): : 877 - 898
  • [8] Convergence of a proximal point algorithm for maximal monotone operators in Hilbert spaces
    Zhiqiang Wei
    Guohong Shi
    [J]. Journal of Inequalities and Applications, 2012
  • [9] Convergence of a proximal point algorithm for maximal monotone operators in Hilbert spaces
    Wei, Zhiqiang
    Shi, Guohong
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2012,
  • [10] CONVERGENCE OF MODIFIED PROXIMAL POINT ALGORITHM IN CAT(0) SPACES
    Weng, Sheng Quan
    Wu, Ding Ping
    Liou, Yeong-Cheng
    Song, Fei
    [J]. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2020, 21 (10) : 2287 - 2298
12345