Rates of asymptotic regularity for the alternating Halpern-Mann iteration

被引：5

作者：

Leustean, Laurentiu ^{[1
,3
,4
]}

Pinto, Pedro ^{[2
]}

机构：

[1] Univ Bucharest, Fac Math & Comp Sci, LOS, Bucharest, Romania

[2] Tech Univ Darmstadt, Dept Math, Darmstadt, Germany

[3] Romanian Acad, Sim Stoilow Inst Math, Bucharest, Romania

[4] Inst Log & Data Sci, Bucharest, Romania

来源：

OPTIMIZATION LETTERS | 2024年 / 18卷 / 02期

关键词：

Mann iteration; Halpern iteration; Rates of asymptotic regularity; Uniform convexity; Proof mining; STRONG-CONVERGENCE; NONEXPANSIVE-MAPPINGS; ALGORITHMS;

D O I：

10.1007/s11590-023-02002-y

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 extend to UCW-hyperbolic spaces the quantitative asymptotic regularity results for the alternating Halpern-Mann iteration obtained by Dinis and the second author for CAT(0) spaces. These results are new even for uniformly convex normed spaces. Furthermore, for a particular choice of the parameter sequences, we compute linear rates of asymptotic regularity in W-hyperbolic spaces and quadratic rates of T- and U-asymptotic regularity in CAT(0) spaces.

引用

页码：529 / 543

页数：15

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