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

页码：70 / 90

页数：21

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