基于非Lipschitz步长策略的临近分裂可行问题的强收敛性研究  

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

作　　者：马小军 陈富 贾芝福 Ma Xiaojun;Chen Fu;Jia Zhifu(School of Mathematics and Statistics,Shanxi Datong University,Shanxi Datong 037009;Suqian College,Jiangsu Suqian 223800)

机构地区：[1]山西大同大学,山西大同037009 [2]宿迁学院,江苏宿迁223800

出　　处：《数学物理学报（A辑）》2024年第4期1052-1065,共14页Acta Mathematica Scientia

基　　金：山西大同大学人才引进科研启动(2023-B-06,202303021222208);宿迁市科技计划项目(K202332);国家自然科学基金(12172266,61803241)。

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.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.

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 

分 类 号：O299[理学—应用数学]