Abstract
This paper deals with a class of inertial gradient projection methods for solving a variational inequality problem involving pseudomonotone and non-Lipschitz mappings in Hilbert spaces. The proposed algorithm incorporates inertial techniques and the projection and contraction method. The weak convergence is proved without the condition of the Lipschitz continuity of the mappings. Meanwhile, the linear convergence of the algorithm is established under strong pseudomonotonicity and Lipschitz continuity assumptions. The main results obtained in this paper extend and improve some related works in the literature.
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Thong, D.V. Modified Inertial Projection Method for Solving Pseudomonotone Variational Inequalities with Non-Lipschitz in Hilbert Spaces. Acta. Math. Sin.-English Ser. 39, 2374–2392 (2023). https://doi.org/10.1007/s10114-023-2080-3
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DOI: https://doi.org/10.1007/s10114-023-2080-3
Keywords
- Inertial method
- projection and contraction method
- variational inequality problem
- pseudomonotone mapping
- convergence rate