多输出集分割可行性问题的两种松弛 CQ 方法

IF 1 3区数学 Q1 MATHEMATICS

Bulletin of the Malaysian Mathematical Sciences Society Pub Date : 2024-02-27 DOI:10.1007/s40840-023-01647-3

Nguyen Thi Thu Thuy, Tran Thanh Tung

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引用次数: 0

摘要

本文提出了两种具有非惯性步长和惯性步长的松弛 CQ 算法，用于求解无限维实希尔伯特空间中具有多个输出集的分割可行性问题（SFPMOS）。步长是动态确定的，不需要关于算子规范的先验信息。此外，所提出的算法被证明能强烈收敛到 SFPMOS 的最小规范解。我们还介绍了我们的主要结果在解决分裂可行性问题中的一些应用。最后，我们给出了两个数值示例，与文献中的现有算法相比，说明了我们算法的效率和实现。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Two Relaxed CQ Methods for the Split Feasibility Problem with Multiple Output Sets

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Two Relaxed CQ Methods for the Split Feasibility Problem with Multiple Output Sets

In this paper, two relaxed CQ algorithms with non-inertial and inertial steps are proposed for solving the split feasibility problems with multiple output sets (SFPMOS) in infinite-dimensional real Hilbert spaces. The step size is determined dynamically without requiring prior information about the operator norm. Furthermore, the proposed algorithms are proven to converge strongly to the minimum-norm solution of the SFPMOS. Some applications of our main results regarding the solution of the split feasibility problem are presented. Finally, we give two numerical examples to illustrate the efficiency and implementation of our algorithms in comparison with existing algorithms in the literature.

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来源期刊

Bulletin of the Malaysian Mathematical Sciences Society 数学-数学

CiteScore

2.40

自引率

8.30%

发文量

176

审稿时长

3 months

期刊介绍： This journal publishes original research articles and expository survey articles in all branches of mathematics. Recent issues have included articles on such topics as Spectral synthesis for the operator space projective tensor product of C*-algebras; Topological structures on LA-semigroups; Implicit iteration methods for variational inequalities in Banach spaces; and The Quarter-Sweep Geometric Mean method for solving second kind linear fredholm integral equations.