求解多集分裂可行问题的线搜索两步投影法  

Two-Step Projection Methods with Linear-Search Technique for Solving the Multiple-Sets Split Feasibility Problem

作　　者：薛中会 周晓中[1] XUE Zhonghui;ZHOU Xiaozhong(Basic Department,Shanghai Publishing and Printing College,Shanghai 200093,China;College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海出版印刷高等专科学校基础部,上海200093 [2]上海理工大学理学院,上海200093

出　　处：《河南大学学报（自然科学版）》2021年第6期750-756,共7页Journal of Henan University:Natural Science

基　　金：国家自然科学基金资助项目(11171221,21203055)。

摘　　要：针对多集分裂可行问题提出了一种可变步长的双外推梯度投影算法.与现有的投影法相比,新算法采用最优步长来更新每次迭代的投影域,以保证下一次迭代更接近解集.在适当条件下,证明了算法的收敛性.基本的数值实验表明,该算法是有效的,而且比现有的投影法收敛更快.In this paper,we propose a new method for solving the multiple-sets split feasibility problem by adopting variable steps sizes.Compared with the existing projection method for solving the problem,the projection region in this new algorithm is modified which makes an optimal step size available at each iteration and hence guarantees that the next iteration is more closer to the solution set.Under mild conditions,we show the convergence of the method.Preliminary numerical experiment shows that this method is more efficient and promising than the existing projection method.

关 键 词：多集分裂可行问题 最优步长 投影算法 收敛性 

分 类 号：O221[理学—运筹学与控制论]