ABSTRACT

The purpose of this paper is to study the convergence analysis of an iterative algorithm with inertial extrapolation step for finding an approximate solution of split monotone inclusion problem in real Hilbert spaces. Weak convergence of the sequence of iterates generated from the proposed method is obtained under some mild assumptions. Some special cases of the general problem are given and we give some numerical implementations to support the theoretical analysis and give justification for the addition of the extrapolation step in the proposed method.

中文翻译：

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分解单调包含问题的惯性外推法

摘要

本文的目的是研究具有惯性外推步骤的迭代算法的收敛性分析，以找到真实希尔伯特空间中分裂单调包含问题的近似解。在一些温和的假设下，从所提出的方法生成的迭代序列的收敛性较弱。给出了一般问题的一些特殊情况，并给出了一些数值方法来支持理论分析，并为所提出的方法中增加外推步骤提供了理由。