Two New Splitting Methods for Three-Operator Monotone Inclusions in Hilbert Spaces

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Set-Valued and Variational Analysis Pub Date : 2024-08-05 DOI:10.1007/s11228-024-00730-6

Van Dung Nguyen, Nguyen The Vinh

引用次数: 0

Abstract

In this paper, we propose two new unified splitting methods for monotone inclusion problems with three operators in real Hilbert spaces. These methods are based on the combination of Douglas-Rachford method and other methods, forward-backward-forward method and reflected-forward-backward method. The weak convergence of new algorithms under standard assumptions is established. We also give some numerical examples to demonstrate the efficiency of the proposed methods.

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希尔伯特空间中三操作单调夹杂的两种新分割方法

本文针对实希尔伯特空间中三个算子的单调包含问题提出了两种新的统一分裂方法。这些方法基于 Douglas-Rachford 方法和其他方法、前向-后向-前向方法和反射-前向-后向方法的组合。新算法在标准假设条件下的弱收敛性得到了证实。我们还给出了一些数值示例来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

Set-Valued and Variational Analysis MATHEMATICS, APPLIED-

CiteScore

2.90

自引率

6.20%

发文量

审稿时长

>12 weeks

期刊介绍： The scope of the journal includes variational analysis and its applications to mathematics, economics, and engineering; set-valued analysis and generalized differential calculus; numerical and computational aspects of set-valued and variational analysis; variational and set-valued techniques in the presence of uncertainty; equilibrium problems; variational principles and calculus of variations; optimal control; viability theory; variational inequalities and variational convergence; fixed points of set-valued mappings; differential, integral, and operator inclusions; methods of variational and set-valued analysis in models of mechanics, systems control, economics, computer vision, finance, and applied sciences. High quality papers dealing with any other theoretical aspect of control and optimization are also considered for publication.