Fast convergent double inertial subgradient extragradient algorithm with self-adaptive step size for variational inequalities and fixed point problems in Hilbert spaces

In this paper, we propose a double inertial subgradient extragradient method for solving variational inequalities and fixed point problems in Hilbert spaces. We add a parameter in the second step projection to adjust the step size, thereby increasing the convergence rate of the proposed algorithm. I...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 475; p. 117016
Main Authors: Li, Min, Xie, Zhongbing
Format: Journal Article
Language:English
Published: Elsevier B.V 15.03.2026
Subjects:
fixed point
Hilbert space
inertial method
subgradient extragradient method
variational inequality
47H10
65K15
fixed point
subgradient extragradient method
Hilbert space
variational inequality
47H05
inertial method
54H25
ISSN:0377-0427
Online Access:Get full text
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Summary:In this paper, we propose a double inertial subgradient extragradient method for solving variational inequalities and fixed point problems in Hilbert spaces. We add a parameter in the second step projection to adjust the step size, thereby increasing the convergence rate of the proposed algorithm. In addition, we make appropriate improvements based on the common self adaptive rules. Finally, through numerical experiments, we not only verify the effectiveness of the added parameters, but also show that our algorithm has better convergence behavior than other known results.
ISSN:0377-0427
DOI:10.1016/j.cam.2025.117016