In this paper, we propose a new algorithm with inertial term and self-adaptive stepsize for solving the split variational inclusion problem (denoted by SVIP) in real Hilbert spaces. Under suitable conditions imposed on the parameters, we prove that our iterative scheme converges strongly to an element of the solution set of SVIP without the prior knowledge of the operator norm. Furthermore, we demonstrate that our suggested algorithm is efficient and achievable through some numerical experiments.

中文翻译：

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一种求解希尔伯特空间分裂变分包含问题的自适应步长的强收敛粘性惯性算法

在本文中，我们提出了一种具有惯性项和自适应步长的新算法来解决实希尔伯特空间中的分裂变分包含问题（用SVIP表示）。在对参数施加适当的条件下，我们证明了我们的迭代方案可以在不先验算子范数的情况下强烈收敛到 SVIP 解集的一个元素。此外，我们通过一些数值实验证明了我们建议的算法是有效且可实现的。