A modified Riemannian Halpern algorithm for nonexpansive mappings on Hadamard manifolds. (9th December 2022)

• Record Type: Journal Article
• Authors: Yao, Teng-Teng; Li, Ying-Hui; Zhang, Yong-Shuai; Zhao, Zhi
• Is Part Of: Optimization. Volume 71:Number 13(2022)
• Page Start: 3797
• Page End: 3817
• Publication Date: 2022-12-09
• Subjects: Nonexpansive mapping -- fixed point -- Halpern algorithm -- Hadamard manifold; 47H09 -- 65K05 -- 90C25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1914036
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we are concerned with the problem of finding fixed points of nonexpansive mappings on Hadamard manifolds. To solving this kind of problem, a modified Riemannian Halpern algorithm, which is a natural generalization of a modified Halpern algorithm in Euclidean space is proposed. By giving some mild assumptions and necessary lemmas, the global convergence of the proposed algorithm is established. Finally, when the problem is solved in the framework of Hadamard manifolds, the numerical experiments show the effectiveness of the proposed algorithm, especially in computational time and number of iterations.