Abstract
In this article, we propose an inertial and a viscosity iterative method for solving variational inequality problem on Hadamard manifolds. The iterative algorithm is inspired by Tseng’s extragradient method with a self-adaptive procedure which generates dynamic step-sizes converging to a positive constant. The proposed method does not require the knowledge of the Lipschitz constant as well as the sequential weak continuity of the corresponding operator. Under a pseudomono-tone assumption on the underlying vector field, we establish a convergence result for solving a pseudomonotone variational inequality and fixed point problems of nonexpansive mapping under some mild assump-tions. Finally, we present some fundamental experiment to illustrate the numerical behavior of our proposed method. The result discussed in this article extends and complements many related results in the literature.
Original language | English |
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Pages (from-to) | 178-199 |
Number of pages | 22 |
Journal | Proceedings of the Institute of Mathematics and Mechanics |
Volume | 50 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2024 |
Externally published | Yes |
Keywords
- Hadamard mani-fold
- Riemannian manifold
- Tseng’s method
- self-adaptive method
- variational inequality problem