Fast relaxed inertial Tseng’s method-based algorithm for solving variational inequality and fixed point problems in Hilbert spaces

• Published in: Journal of computational and applied mathematics Vol. 418; p. 114739
• Main Authors: Thong, Duong Viet, Liu, Lu-Lu, Dong, Qiao-Li, Van Long, Luong, Tuan, Pham Anh
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.01.2023
• Subjects: Convergence rate; Demicontractive mapping; Fixed point problem; Pseudomonotone mapping; Relaxed inertial Tseng’s method; Variational inequality problem; 65K15; Fixed point problem; 68W10; Variational inequality problem; Convergence rate; Demicontractive mapping; 47H05; 47J25; Relaxed inertial Tseng’s method; 65Y05; Pseudomonotone mapping
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2022.114739

Motivated and inspired by the works of Ceng et al. (2010) and Yao and Postolache (2012), we first study a relaxed inertial Tseng’s method for finding a common element of the set of solution of a pseudomonotone, Lipschitz-continuous variational inequality problem and the set of fixed points of an κ-demicontractive mapping in real Hilbert spaces. The strong convergence of the algorithm is proved with conditions weaker than the conditions of other methods studied in the literature. Next, we also obtain an R-linear convergence rate of relaxed inertial Tseng’s method under strong pseudomonotonicity and Lipschitz continuity assumptions of the variational inequality mapping. As far as we know, these results have not been considered before in the literature. Finally, some numerical examples illustrate the effectiveness of our algorithms.