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Volume 14, Issue 1
Iterative Method with Inertia for Variational Inequalities on Hadamard Manifolds with Lower Bounded Curvature

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

DOI: 10.4208/eajam.2023-093.130723

East Asian J. Appl. Math., 14 (2024), pp. 195-222.

Published online: 2024-01

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  • Abstract

In this paper, we are concerned with solving variational inequalities on Hadamard manifolds, the curvature of which is bounded from below. The underlying vector field is assumed to be continuous and pseudomonotone. By combining the hyperplane projection method and the inertial extrapolation technique, a Halpern-type method is proposed. Under some mild assumptions, global convergence of the proposed algorithm is established. Numerical experiments are reported to show the efficiency of the proposed algorithm.

  • Keywords

Variational inequality, pseudomonotone vector field, Hadamard manifold, hyperplane projection method, inertial term.

  • AMS Subject Headings

47J20, 65K05, 90C33

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-14-195, author = {Yao , Teng-TengJin , Xiao-Qing and Zhao , Zhi}, title = {Iterative Method with Inertia for Variational Inequalities on Hadamard Manifolds with Lower Bounded Curvature}, journal = {East Asian Journal on Applied Mathematics}, year = {2024}, volume = {14}, number = {1}, pages = {195--222}, abstract = {

In this paper, we are concerned with solving variational inequalities on Hadamard manifolds, the curvature of which is bounded from below. The underlying vector field is assumed to be continuous and pseudomonotone. By combining the hyperplane projection method and the inertial extrapolation technique, a Halpern-type method is proposed. Under some mild assumptions, global convergence of the proposed algorithm is established. Numerical experiments are reported to show the efficiency of the proposed algorithm.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2023-093.130723 }, url = {http://global-sci.org/intro/article_detail/eajam/22325.html} }
TY - JOUR T1 - Iterative Method with Inertia for Variational Inequalities on Hadamard Manifolds with Lower Bounded Curvature AU - Yao , Teng-Teng AU - Jin , Xiao-Qing AU - Zhao , Zhi JO - East Asian Journal on Applied Mathematics VL - 1 SP - 195 EP - 222 PY - 2024 DA - 2024/01 SN - 14 DO - http://doi.org/10.4208/eajam.2023-093.130723 UR - https://global-sci.org/intro/article_detail/eajam/22325.html KW - Variational inequality, pseudomonotone vector field, Hadamard manifold, hyperplane projection method, inertial term. AB -

In this paper, we are concerned with solving variational inequalities on Hadamard manifolds, the curvature of which is bounded from below. The underlying vector field is assumed to be continuous and pseudomonotone. By combining the hyperplane projection method and the inertial extrapolation technique, a Halpern-type method is proposed. Under some mild assumptions, global convergence of the proposed algorithm is established. Numerical experiments are reported to show the efficiency of the proposed algorithm.

Teng-Teng Yao, Xiao-Qing Jin & Zhi Zhao. (2024). Iterative Method with Inertia for Variational Inequalities on Hadamard Manifolds with Lower Bounded Curvature. East Asian Journal on Applied Mathematics. 14 (1). 195-222. doi:10.4208/eajam.2023-093.130723
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