分裂可行性问题的一个惯性共轭梯度投影法

数学物理学报 ›› 2024, Vol. 44 ›› Issue (4): 1066-1079.

分裂可行性问题的一个惯性共轭梯度投影法

简金宝,代钰,尹江华^*()

广西民族大学数学与物理学院, 广西应用数学中心南宁 530006

收稿日期:2023-10-05 修回日期:2024-02-01 出版日期:2024-08-26 发布日期:2024-07-26
通讯作者: *尹江华, E-mail: jianghuayin1017@126.com
基金资助:
广西自然科学基金(2023GXNSFBA026029);广西科技计划项目(桂科AD23023001);广西高校中青年教师基础能力提升项目(2023KY0168);广西民族大学校级引进人才科研启动项目(2022KJQD03)

An Inertial Conjugate Gradient Projection Method for the Split Feasibility Problem

Jian Jinbao,Dai Yu,Yin Jianghua^*()

School of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Minzu University, Nanning 530006

Received:2023-10-05 Revised:2024-02-01 Online:2024-08-26 Published:2024-07-26
Supported by:
Natural Science Foundation of Guangxi(2023GXNSFBA026029);Guangxi Science and Technology Program (AD23023001);Middle-aged and Young Teachers' Basic Ability Promotion Project of Guangxi(2023KY0168);Research Project of Guangxi Minzu University(2022KJQD03)

摘要/Abstract

摘要：

基于分裂可行性问题的凸约束非线性单调方程组等价问题, 提出了一个新的惯性共轭梯度投影法. 该算法不需要计算矩阵 ${A^\top}A$ 的最大特征值和多次的复杂投影. 在较弱的条件下, 证明了算法的全局收敛性, 并分析了算法的收敛率. 数值试验结果初步表明算法是有效的和鲁棒的.

关键词: 分裂可行性问题, 惯性技术, 共轭梯度投影法, 全局收敛性, 收敛率

Abstract:

Based on a convex constrained nonlinear monotone equations equivalent to the split feasibility problem, in this paper, a novel inertial conjugate gradient projection method is proposed. The presented method does not calculate the maximum eigenvalue of the matrix ${A^\top}A$ and the complex projections of multiple times. Under mild conditions, the global convergence of the proposed method is proved, and its rate of convergence is analyzed. Numerical experiments show that the proposed method is efficient and robust.

Key words: Split feasibility problem, Inertial technique, Conjugate gradient projection algorithm, Global convergence, Convergence rate

中图分类号:

O221.2

简金宝, 代钰, 尹江华. 分裂可行性问题的一个惯性共轭梯度投影法[J]. 数学物理学报, 2024, 44(4): 1066-1079.

Jian Jinbao, Dai Yu, Yin Jianghua. An Inertial Conjugate Gradient Projection Method for the Split Feasibility Problem[J]. Acta mathematica scientia,Series A, 2024, 44(4): 1066-1079.

图/表 1

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