一种新的步长梯度投影方法用于分割可行性问题。

IF 1.6 3区 数学 Q1 Mathematics
Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-05-18 DOI:10.1186/s13660-018-1712-0
Pattanapong Tianchai
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引用次数: 2

摘要

本文基于Moudafi的黏度近似法,提出了一种不依赖于相关矩阵逆和相关矩阵的最大特征值(或自伴随算子的谱半径)的梯度投影迭代方案。即在实希尔伯特空间的给定闭凸子集中找到一个点,使得它在有界线性算子下的像属于另一个实希尔伯特空间的给定闭凸子集。在适当的参数条件下,我们提出并分析了该迭代格式,从而得到了SFP的另一个强收敛定理。本文的结果改进和推广了Tian和Zhang (J. Inequal)的主要结果。applied . 2017:Article ID 13, 2017), and Tang et al. (Acta Math.)科学通报,2016,36(2):602-613)(在单步正则化方法中)使用新的步长,以及许多其他方法。最后,通过数值结果给出了所提SFP的算例。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Gradient projection method with a new step size for the split feasibility problem.

In this paper, we introduce an iterative scheme using the gradient projection method with a new step size, which is not depend on the related matrix inverses and the largest eigenvalue (or the spectral radius of the self-adjoint operator) of the related matrix, based on Moudafi's viscosity approximation method for solving the split feasibility problem (SFP), which is to find a point in a given closed convex subset of a real Hilbert space such that its image under a bounded linear operator belongs to a given closed convex subset of another real Hilbert space. We suggest and analyze this iterative scheme under some appropriate conditions imposed on the parameters such that another strong convergence theorems for the SFP are obtained. The results presented in this paper improve and extend the main results of Tian and Zhang (J. Inequal. Appl. 2017:Article ID 13, 2017), and Tang et al. (Acta Math. Sci. 36B(2):602-613, 2016) (in a single-step regularized method) with a new step size, and many others. The examples of the proposed SFP are also shown through numerical results.

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来源期刊
Journal of Inequalities and Applications
Journal of Inequalities and Applications MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
3.30
自引率
6.20%
发文量
136
审稿时长
3 months
期刊介绍: The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.
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