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On Mann implicit composite subgradient extragradient methods for general systems of variational inequalities with hierarchical variational inequality constraints
- Source :
- Journal of Inequalities and Applications, Vol 2022, Iss 1, Pp 1-28 (2022)
- Publication Year :
- 2022
- Publisher :
- SpringerOpen, 2022.
-
Abstract
- Abstract In a real Hilbert space, let the VIP, GSVI, HVI, and CFPP denote a variational inequality problem, a general system of variational inequalities, a hierarchical variational inequality, and a common fixed-point problem of a countable family of uniformly Lipschitzian pseudocontractive mappings and an asymptotically nonexpansive mapping, respectively. We design two Mann implicit composite subgradient extragradient algorithms with line-search process for finding a common solution of the CFPP, GSVI, and VIP. The suggested algorithms are based on the Mann implicit iteration method, subgradient extragradient method with line-search process, and viscosity approximation method. Under mild assumptions, we prove the strong convergence of the suggested algorithms to a common solution of the CFPP, GSVI, and VIP, which solves a certain HVI defined on their common solutions set.
Details
- Language :
- English
- ISSN :
- 1029242X
- Volume :
- 2022
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Journal of Inequalities and Applications
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.2ce79be861c44b4dafdbdf8ec5080b30
- Document Type :
- article
- Full Text :
- https://doi.org/10.1186/s13660-022-02813-0