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<p>In this paper, we propose an inertial splitting algorithm to compute a zero of the sum of a maximally monotone operator and a monotone and Lipschitz continuous operator. This work aims to extend reflected-forward-backward method by using inertial effects. We prove the convergence of the algorithm in a Hilbert space setting and show that the range of step size can be improved. The linear convergence of the proposed method is obtained under a condition akin to strong monotonicity. We also give some simple numerical experiments to demonstrate the efficiency of the proposed algorithm.</p>

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An inertial reflected-forward-backward splitting method for monotone inclusions with improved step size

  • 期刊论文

  • 发表日期：

    2026年1月8日

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  • Van Dung Nguyen,
  • Hoang Thi Kim Hoa

摘要

In this paper, we propose an inertial splitting algorithm to compute a zero of the sum of a maximally monotone operator and a monotone and Lipschitz continuous operator. This work aims to extend reflected-forward-backward method by using inertial effects. We prove the convergence of the algorithm in a Hilbert space setting and show that the range of step size can be improved. The linear convergence of the proposed method is obtained under a condition akin to strong monotonicity. We also give some simple numerical experiments to demonstrate the efficiency of the proposed algorithm.