A modification of the forward–backward splitting method for monotone inclusions

IF 1.3 4区数学 Q2 MATHEMATICS, APPLIED

Optimization Letters Pub Date : 2024-06-18 DOI:10.1007/s11590-024-02128-7

Van Dung Nguyen

引用次数: 0

Abstract

In this work, we propose a new splitting method for monotone inclusion problems with three operators in real Hilbert spaces, in which one is maximal monotone, one is monotone-Lipschitz and one is cocoercive. By specializing in two operator inclusion, we recover the forward–backward and the generalization of the reflected-forward–backward splitting methods as particular cases. The weak convergence of the algorithm under standard assumptions is established. The linear convergence rate of the proposed method is obtained under an additional condition like the strong monotonicity. We also give some theoretical comparisons to demonstrate the efficiency of the proposed method.

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单调夹杂物前向后分裂法的修正

在这项工作中，我们提出了一种新的拆分方法，用于实希尔伯特空间中三个算子的单调包含问题，其中一个算子是最大单调的，一个是单调-利普希兹的，一个是可塞的。通过对两个算子包含的特殊化，我们恢复了作为特殊情况的前向后向和广义反射前向后向分裂方法。在标准假设条件下，算法的弱收敛性得以确定。在强单调性等附加条件下，我们得到了所提方法的线性收敛率。我们还给出了一些理论比较，以证明所提方法的效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Optimization Letters 管理科学-应用数学

CiteScore

3.40

自引率

6.20%

发文量

116

审稿时长

9 months

期刊介绍： Optimization Letters is an international journal covering all aspects of optimization, including theory, algorithms, computational studies, and applications, and providing an outlet for rapid publication of short communications in the field. Originality, significance, quality and clarity are the essential criteria for choosing the material to be published. Optimization Letters has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time one of the most striking trends in optimization is the constantly increasing interdisciplinary nature of the field. Optimization Letters aims to communicate in a timely fashion all recent developments in optimization with concise short articles (limited to a total of ten journal pages). Such concise articles will be easily accessible by readers working in any aspects of optimization and wish to be informed of recent developments.