This paper studies the forward–reflected–backward splitting algorithm with momentum terms for monotone inclusion problem of the sum of a maximal monotone and Lipschitz continuous monotone operators in Hilbert spaces. The forward–reflected–backward splitting algorithm is an interesting algorithm for inclusion problems with the sum of maximal monotone and Lipschitz continuous monotone operators due to the inherent feature of one forward evaluation and one backward evaluation per iteration it possesses. The results in this paper further explore the convergence behavior of the forward–reflected–backward splitting algorithm with momentum terms. We obtain weak, linear, and strong convergence results under the same inherent feature of one forward evaluation and one backward evaluation at each iteration. Numerical results show that forward–reflected–backward splitting algorithms with momentum terms are efficient and promising over some related splitting algorithms in the literature.

本文研究了希尔伯特空间中最大单调算子与Lipschitz连续单调算子之和的单调包含问题的带有动量项的前向-反射-后向分裂算法。前向-反射-后向分裂算法是一种有趣的算法，用于解决最大单调算子和 Lipschitz 连续单调算子之和的包含问题，因为它具有每次迭代一次前向评估和一次后向评估的固有特征。本文的结果进一步探讨了带有动量项的前向-反射-后向分裂算法的收敛行为。在每次迭代中一次前向评估和一次后向评估的相同固有特征下，我们获得了弱收敛、线性收敛和强收敛结果。数值结果表明，带有动量项的前向-反射-后向分裂算法比文献中的一些相关分裂算法更加高效且有前景。