A new double inertial subgradient extragradient method for solving a non-monotone variational inequality problem in Hilbert space

Ziqi Zhu; Kaiye Zheng; Shenghua Wang; Ziqi Zhu; Kaiye Zheng; Shenghua Wang

doi:10.3934/math.20241020

AIMS Mathematics

2024, Volume 9, Issue 8: 20956-20975. doi: 10.3934/math.20241020

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Research article

A new double inertial subgradient extragradient method for solving a non-monotone variational inequality problem in Hilbert space

Department of Mathematics and Physics, Hebei Key Laboratory of Physics and Energy Technology, North China Electric Power University, Baoding 071003, China

Received: 01 April 2024 Revised: 15 June 2024 Accepted: 20 June 2024 Published: 28 June 2024
MSC : 47H05, 47J20, 65K15

In this paper, we introduced a new double inertial subgradient extragradient method for solving a variational inequality problem in Hilbert space. In our method, the mapping needed not to satisfy any assumption of monotonicity and two different self-adaptive step sizes were used for avoiding the need of Lipschitz constant of the mapping. The strong convergence of the proposed method was proved under some new conditions. Finally, some numerical examples were presented to illustrate the convergence of our method and compare with some related methods in the literature.
- variational inequality,
- subgradient extragradient method,
- strong convergence,
- inertial method
Citation: Ziqi Zhu, Kaiye Zheng, Shenghua Wang. A new double inertial subgradient extragradient method for solving a non-monotone variational inequality problem in Hilbert space[J]. AIMS Mathematics, 2024, 9(8): 20956-20975. doi: 10.3934/math.20241020

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Abstract

In this paper, we introduced a new double inertial subgradient extragradient method for solving a variational inequality problem in Hilbert space. In our method, the mapping needed not to satisfy any assumption of monotonicity and two different self-adaptive step sizes were used for avoiding the need of Lipschitz constant of the mapping. The strong convergence of the proposed method was proved under some new conditions. Finally, some numerical examples were presented to illustrate the convergence of our method and compare with some related methods in the literature.

References

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