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Iterative algorithm with self-adaptive step size for approximating the common solution of variational inequality and fixed point problems.
- Source :
-
Optimization . Mar2023, Vol. 72 Issue 3, p677-711. 35p. - Publication Year :
- 2023
-
Abstract
- In this paper, we propose and study new inertial viscosity Tseng's extragradient algorithms with self-adaptive step size to solve the variational inequality problem (VIP) and the fixed point problem (FPP) in Hilbert spaces. Our proposed methods involve a projection onto a half-space and self-adaptive step size. We prove that the sequence generated by our proposed methods converges strongly to a common solution of the VIP and FPP of an infinite family of strict pseudo-contractive mappings in Hilbert spaces under some mild assumptions when the underlying operator is monotone and Lipschitz continuous. Furthermore, we apply our results to find a common solution of VIP and zero-point problem (ZPP) for an infinite family of maximal monotone operators. Finally, we provide some numerical experiments of the proposed methods in comparison with other existing methods in the literature. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MONOTONE operators
*NONEXPANSIVE mappings
*HILBERT space
*ALGORITHMS
Subjects
Details
- Language :
- English
- ISSN :
- 02331934
- Volume :
- 72
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 162144672
- Full Text :
- https://doi.org/10.1080/02331934.2021.1981897