Geodesic
Subgradient-like extragradient algorithms for systems of variational inequalities with constraints
Filomat, Tome 37 (2023) no. 21, p. 7181

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DOI

In this paper, we introduce a modified viscosity subgradient-like extragradient implicit rule with line-search process for finding a solution of a general system of variational inequalities (GSVI) with a variational inequality (VIP) and a fixed-point (FPP) constraints in Hilbert spaces. The suggested algorithms are based on the subgradient extragradient method with line-search process, hybrid Mann implicit iteration method, and composite viscosity approximation method. Under suitable restrictions, we demonstrate the strong convergence of the suggested algorithm to a solution of the GSVI with the VIP and FPP constraints, which is a unique solution of a certain hierarchical variational inequality.
DOI : 10.2298/FIL2321181C
Classification : 47H09, 47J20, 47H10, 47J25
Keywords: subgradient-like extragradient algorithm, variational inequality, asymptotically nonexpansive mapping, projection 
Lu-Chuan Ceng; Tzu-Chien Yin. Subgradient-like extragradient algorithms for systems of variational inequalities with constraints. Filomat, Tome 37 (2023) no. 21, p. 7181 . doi: 10.2298/FIL2321181C
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     title = {Subgradient-like extragradient algorithms for systems of variational inequalities with constraints},
     journal = {Filomat},
     pages = {7181 },
     year = {2023},
     volume = {37},
     number = {21},
     doi = {10.2298/FIL2321181C},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2321181C/}
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