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<p>This paper designs forward-reflected-backward algorithms with two inertial extrapolation steps to solve variational inequalities of quasi-monotone operators. We consider forward-reflected algorithms with two inertial extrapolation steps for constant and nondecreasing self-adaptive step sizes. The algorithms also feature one projection and operator evaluation at each inertial step per iteration. We give weak convergence results for the two proposed algorithms. Strong convergence and linear convergence results are also achieved under standard conditions. Numerical results from image processing confirm the superiority of our algorithms over other related ones in the literature.</p>

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Forward-reflected-backward algorithms with double inertial extrapolations for variational inequalities with applications to image processing

  • 期刊论文

  • 发表日期：

    2025年5月20日

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  • Yonghong Yao,
  • Abubakar Adamu,
  • Yekini Shehu,
  • Jen-Chih Yao

摘要

This paper designs forward-reflected-backward algorithms with two inertial extrapolation steps to solve variational inequalities of quasi-monotone operators. We consider forward-reflected algorithms with two inertial extrapolation steps for constant and nondecreasing self-adaptive step sizes. The algorithms also feature one projection and operator evaluation at each inertial step per iteration. We give weak convergence results for the two proposed algorithms. Strong convergence and linear convergence results are also achieved under standard conditions. Numerical results from image processing confirm the superiority of our algorithms over other related ones in the literature.