分裂可行问题的两种强收敛CQ算法(英文)  

Two Strongly Convergent CQ Algorithms for Split Feasibility Problem

作　　者：党亚峥[1] 薛中会[2] 高岩[1] 

机构地区：[1]上海理工大学管理学院,上海200093 [2]河南理工大学理化学院,焦作454001

出　　处：《工程数学学报》2015年第2期298-306,共9页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(11171221;61403255);the Doctoral Program Foundation of Institutions of Higher Education of China(20123120110004);the China Coal Industry Association 2011 Annual Scientific and Technical Guidance Programs(MTKJ-2011-404);the Natural Science Foundation of Shanghai(14ZR1429200);the Shanghai Leading Academic Discipline Project(XTK X2012);the Innovation Program of Shanghai Municipal Education Commission(15ZZ073);the Doctoral Starting Projection of the University of Shanghai for Science and Technology(ID-10-303-002);the Young Teacher Training Projection Program of Shanghai for Science and Technology

摘　　要：为保证Hilbert空间中求解分裂可行问题迭代算法的强收敛性,本文首先通过引入三个参数序列提出了求解分裂可行问题的改进CQ算法,并在较弱的条件下证明了算法的强收敛性.然后改进算法中的一个算子,即选择另外一个参数序列嵌入到一个算子里,得到了一种新的算法.在参数序列满足一定条件下也证明了算法的强收敛性.本文拓展了现已有的相关研究成果.In thins paper, in order to ensure the strong convergence of the iterative procedure for solving split feasibility problem in a a modified CQ algorithm by introducing real Hilbert space. We firstly construct three parametric sequences and prove its strong convergence under some weak conditions. Furthermore, we put another parametric sequence in one operator in the presented algorithm to get a new Mgorithm, and also prove its strong convergence under some conditions on the parametric sequence. The results in this paper improve and extend the corresponding results.

关 键 词：分裂可行问题 改进CQ算法 强收敛性 

分 类 号：O224.1[理学—运筹学与控制论]