This paper aims to obtain a strong convergence result for a Douglas–Rachford splitting method with inertial extrapolation step for finding a zero of the sum of two set-valued maximal monotone operators without any further assumption of uniform monotonicity on any of the involved maximal monotone operators. Furthermore, our proposed method is easy to implement and the inertial factor in our proposed method is a natural choice. Our method of proof is of independent interest. Finally, some numerical implementations are given to confirm the theoretical analysis.

中文翻译：

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两个最大单调算子之和的新的强收敛方法

本文旨在获得具有惯性外推步骤的Douglas-Rachford分裂方法的强收敛结果，以找到两个集值最大单调算子之和的零，而无需进一步假设任何涉及的最大单调算子的一致单调性。此外，我们提出的方法易于实现，并且我们提出的方法中的惯性因子是自然选择。我们的证明方法具有独立利益。最后，给出了一些数值实现来证实理论分析。