On Mann implicit composite subgradient extragradient methods for general systems of variational inequalities with hierarchical variational inequality constraints

Autor: Lu-Chuan Ceng, Jen-Chih Yao, Yekini Shehu
Jazyk: angličtina
Rok vydání: 2022
Předmět:
Zdroj: Journal of Inequalities and Applications, Vol 2022, Iss 1, Pp 1-28 (2022)
Druh dokumentu: article
ISSN: 1029-242X
DOI: 10.1186/s13660-022-02813-0
Popis: 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.
Databáze: Directory of Open Access Journals
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