分裂可行问题(SFP)的投影算法  

THE PROJECTION-TYPE METHODS FOR SOLVING THE SPLIT FEASIBILITY PROBLEM

作　　者：杨庆之[1] 赵金玲[1] 

机构地区：[1]南开大学数学科学学院核心数学与组合数学实验室(LPMC),天津300071

出　　处：《计算数学》2006年第2期121-132,共12页Mathematica Numerica Sinica

基　　金：国家自然科学基金(批准号:10571134)资助项目

摘　　要：本文探讨了分裂可行问题(SFP)的投影算法．我们先定义了(SFP)的反问题(ISFP), 然后利用正交投影性质,给出了(SFP)与(ISFP)及某些投影不动点问题之间的关系．随后, 给出了求解(SFP)的几种正交投影算法,其中包括精确和不精确投影格式．基于变分不等式中投影算法收敛性的证明思路和分裂可行问题的特有形式,证明了这几种算法的收敛性．最后通过几个算例对讨论的方法进行了初步比较．In this paper we study the projection-type methods for solving the split feasibility problem. We define the split feasibility problem and its inverse problem and build the connections between the split feasibility problem, its inverse problem and several fixed point problems containing the projection operators. Based on it, we present several algorithms solving the split feasibility problem, including the exact and inexact schemes. Finally, we perform some numerical experiments, which preliminarily show the behaviors of the algorithms proposed.

关 键 词：SFP ISFP 正交投影 MOORE-PENROSE广义逆 算法 

分 类 号：O241.6[理学—计算数学]