Abstract
In this paper, we propose and study a Bilevel quasimonotone Variational Inequality Problem (BVIP) in the framework of Hilbert space. We introduce a new modified inertial iterative technique with self- adaptive step size for approximating a solution of the BVIP. In addition, we established a strong convergence result of the proposed iterative technique with adaptive step-size conditions without prior knowledge of Lips- chitz's constant of the cost operators as well as the strongly monotonicity coefficient under some standard mild assumptions. Finally, we provide some numerical experiments to demonstrate the efficiency of our proposed methods in comparison with some recently announced results in the literature.
Original language | English |
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Journal | Boletim da Sociedade Paranaense de Matematica |
Volume | 42 |
DOIs | |
Publication status | Published - 2024 |
Externally published | Yes |
Keywords
- Hilbert space
- Variational inequality problem
- inertial technique
- quasimonotone