基于非 Lipschitz 步长策略的临近分裂可行问题的强收敛性研究

数学物理学报 ›› 2024, Vol. 44 ›› Issue (4): 1052-1065.

基于非 Lipschitz 步长策略的临近分裂可行问题的强收敛性研究

马小军¹,陈富¹,贾芝福^2,^*()

¹山西大同大学山西大同 037009
²宿迁学院江苏宿迁 223800

收稿日期:2023-07-20 修回日期:2024-02-25 出版日期:2024-08-26 发布日期:2024-07-26
通讯作者: *贾芝福, E-mail: fzhuangmaxj@163.com
基金资助:
山西大同大学人才引进科研启动(2023-B-06);山西大同大学人才引进科研启动(202303021222208);宿迁市科技计划项目(K202332);国家自然科学基金(12172266);国家自然科学基金(61803241)

Research on a Strong Convergence Theorem for Proximal Split Feasibility Problems with Non-Lipschitz Stepsizes

Ma Xiaojun¹,Chen Fu¹,Jia Zhifu^2,^*()

¹School of Mathematics and Statistics, Shanxi Datong University, Shanxi Datong 037009
²Suqian College, Jiangsu Suqian 223800

Received:2023-07-20 Revised:2024-02-25 Online:2024-08-26 Published:2024-07-26
Supported by:
Startup Foundation for Newly Recruited Employee(2023-B-06);Startup Foundation for Newly Recruited Employee(202303021222208);Suqian Sci Tech Program(K202332);National Natural Science Foundation of China(12172266);National Natural Science Foundation of China(61803241)

摘要/Abstract

摘要：

针对 Hilbert 空间中的临近分裂可行问题, 该文提出了一种惯性粘滞类算法. 其中主要引入了一种非 Lipschitz 步长策略, 其克服了原步长远离零的缺点. 另外, 通过弱化临近映射的完全非扩张性, 证明了修正后算法的强收敛性. 进一步, 将所得的结论应用于分裂均衡问题. 最后, 列举实例充分说明了修正后算法的有效性.

关键词: 临近分裂可行问题, 分裂均衡问题, 非 Lipschitz 连续映射, 粘滞类算法, 强收敛性

Abstract:

In this paper, An inertial viscosity-type algorithm is proposed to solve proximal split feasibility problems in Hilbert spaces. In this algorithm, a non-Lipschitz stepsize rule is given, which overcomes the drawback that the stepsize tends to zero. Further, a strong convergence theorem for our proposed algorithm is established without Lipschitz continuity of the gradient operators. As theoretical applications, the split equilibrium problem is investigated. Finally, numerical experiments are provided for demonstration and comparison.

Key words: Proximal split feasibility problem, Split equilibrium problem, Non-Lipschitz continuity, Viscosity-type algorithm, Strong convergence

中图分类号:

马小军, 陈富, 贾芝福. 基于非 Lipschitz 步长策略的临近分裂可行问题的强收敛性研究[J]. 数学物理学报, 2024, 44(4): 1052-1065.

Ma Xiaojun, Chen Fu, Jia Zhifu. Research on a Strong Convergence Theorem for Proximal Split Feasibility Problems with Non-Lipschitz Stepsizes[J]. Acta mathematica scientia,Series A, 2024, 44(4): 1052-1065.

图/表 4

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