full
search.png

Search

close.png

Cancel

arrow
Volume 16, Issue 4
A Riemannian Inertial Mann Algorithm for Nonexpansive Mappings on Hadamard Manifolds

Teng-Teng Yao, Xiao-Qing Jin & Zhi Zhao

DOI: 10.4208/nmtma.OA-2023-0039

Numer. Math. Theor. Meth. Appl., 16 (2023), pp. 954-967.

Published online: 2023-11

Preview Purchase PDF 1484 18864

Cited by

google scholar semantic scholar
Export citation
  • Abstract

The problem of finding fixed points of nonexpansive mappings on Hadamard manifolds is considered in this paper. To solve this kind of problem, we propose a modified Riemannian Mann algorithm with inertial effect. Under the assumption of existence of fixed points of the nonexpansive mapping, the global convergence of the proposed algorithm is established. To show the efficiency of the proposed algorithm, numerical comparisons with some existing algorithms are reported.

  • Keywords

Nonexpansive mapping, Hadamard manifold, fixed point, inertial Mann algorithm.

  • AMS Subject Headings

647H09, 65K05, 90C25

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{NMTMA-16-954, author = {Yao , Teng-TengJin , Xiao-Qing and Zhao , Zhi}, title = {A Riemannian Inertial Mann Algorithm for Nonexpansive Mappings on Hadamard Manifolds}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2023}, volume = {16}, number = {4}, pages = {954--967}, abstract = {

The problem of finding fixed points of nonexpansive mappings on Hadamard manifolds is considered in this paper. To solve this kind of problem, we propose a modified Riemannian Mann algorithm with inertial effect. Under the assumption of existence of fixed points of the nonexpansive mapping, the global convergence of the proposed algorithm is established. To show the efficiency of the proposed algorithm, numerical comparisons with some existing algorithms are reported.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2023-0039}, url = {http://global-sci.org/intro/article_detail/nmtma/22118.html} }
TY - JOUR T1 - A Riemannian Inertial Mann Algorithm for Nonexpansive Mappings on Hadamard Manifolds AU - Yao , Teng-Teng AU - Jin , Xiao-Qing AU - Zhao , Zhi JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 954 EP - 967 PY - 2023 DA - 2023/11 SN - 16 DO - http://doi.org/10.4208/nmtma.OA-2023-0039 UR - https://global-sci.org/intro/article_detail/nmtma/22118.html KW - Nonexpansive mapping, Hadamard manifold, fixed point, inertial Mann algorithm. AB -

The problem of finding fixed points of nonexpansive mappings on Hadamard manifolds is considered in this paper. To solve this kind of problem, we propose a modified Riemannian Mann algorithm with inertial effect. Under the assumption of existence of fixed points of the nonexpansive mapping, the global convergence of the proposed algorithm is established. To show the efficiency of the proposed algorithm, numerical comparisons with some existing algorithms are reported.

Yao , Teng-TengJin , Xiao-Qing and Zhao , Zhi. (2023). A Riemannian Inertial Mann Algorithm for Nonexpansive Mappings on Hadamard Manifolds. Numerical Mathematics: Theory, Methods and Applications. 16 (4). 954-967. doi:10.4208/nmtma.OA-2023-0039
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard