ABSTRACT

The paper presents four modifications of the inertial forward–backward splitting method for monotone inclusion problems in the framework of real Hilbert spaces. The advantages of our iterative schemes are that the single-valued operator is Lipschitz continuous monotone rather than cocoercive and the Lipschitz constant does not require to be known. The strong convergence of the suggested approaches is obtained under some standard and mild conditions. Finally, several numerical experiments in finite- and infinite-dimensional spaces are proposed to demonstrate the advantages of our algorithms over the existing related ones.

中文翻译：

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求解单调夹杂的惯性前后向方法的强收敛性

摘要

本文提出了在真实希尔伯特空间框架下对单调包含问题的惯性前后分裂方法的四种修改。我们的迭代方案的优点是单值算子是 Lipschitz 连续单调而不是 cocoercive，并且不需要知道 Lipschitz 常数。在一些标准和温和的条件下获得了所建议方法的强收敛性。最后，提出了在有限和无限维空间中的几个数值实验，以证明我们的算法相对于现有相关算法的优势。