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<p>In this paper, we introduce a subgradient extragradient method with double inertial extrapolation steps and self-adaptive step sizes for finding a common solution of the variational inequality problem, involving a pseudo-monotone mapping and Lipschitz continuous operator and the fixed point problem with a quasi-nonexpansive in real Hilbert spaces. Weak convergence theorems are obtained under some appropriate conditions imposed on the parameters. Numerical experiments are given to illustrate the efficiency of our proposed algorithm.</p>

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Subgradient extragradient algorithm with double inertial steps for solving variational inequality problems and fixed point problems in Hilbert spaces

  • 期刊论文

  • 发表日期：

    2025年5月30日

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  • Yi Huang,
  • Liyue You,
  • Gang Cai,
  • Qiao-Li Dong

摘要

In this paper, we introduce a subgradient extragradient method with double inertial extrapolation steps and self-adaptive step sizes for finding a common solution of the variational inequality problem, involving a pseudo-monotone mapping and Lipschitz continuous operator and the fixed point problem with a quasi-nonexpansive in real Hilbert spaces. Weak convergence theorems are obtained under some appropriate conditions imposed on the parameters. Numerical experiments are given to illustrate the efficiency of our proposed algorithm.