求解分裂可行问题的次梯度投影松弛算法  

Subgradient projection relaxed method for solving the split feasibility problem

作　　者：陈进作 王元恒[1] CHEN Jinzuo;WANG Yuanheng(School of Mathematical Sciences,Zhejiang Normal University,Jinhua 321004,China)

机构地区：[1]浙江师范大学数学科学学院,浙江金华321004

出　　处：《浙江师范大学学报（自然科学版）》2024年第1期9-13,共5页Journal of Zhejiang Normal University:Natural Sciences

基　　金：国家自然科学基金资助项目(12171435)。

摘　　要：在无限维Hilbert空间中,区别于现有许多算法中的正交投影,采用次梯度投影法,提出求解分裂可行问题的次梯度投影松弛算法,并利用次梯度算子的cutter性质以及分类讨论的思想,证明了次梯度投影松弛算法生成的序列弱收敛于分裂可行问题的解.Based on subgradient projection instead of the orthogonal projection in many existing algorithms,it was proposed a subgradient projection relaxation algorithm for solving the split feasibility problem in infinite dimension Hilbert spaces.It was proved that the sequence generated by the algorithm was weakly convergent to the solution of the split feasibility problem based on the cutter property of subgradient operator and classified discussion.

关 键 词：分裂可行问题 次梯度投影 松弛算法 弱收敛 

分 类 号：O177.91[理学—数学]