A new halfspace-relaxation projection method for the split feasibility problem

被引：59

作者：

Qu, Biao ^{[1
,2
]}

Xiu, Naihua ^{[1
]}

机构：

[1] Beijing Jiao Tong Univ, Dept Appl Math, Beijing 100044, Peoples R China

[2] Qufu Normal Univ, Inst Operat Res, Shandong 276826, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2008年 / 428卷 / 5-6期

基金：

中国国家自然科学基金;

关键词：

the split feasibility problem; halfspace-relaxation projection method; fully convergent;

D O I：

10.1016/j.laa.2007.03.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let C and Q be nonempty closed convex sets in R-n and R-m respectively, and A an m x n real matrix. The problem, to find x is an element of C with Ax is an element of Q if such x exist, is called the split feasibility problem (SFP). This problem is important in intensity-modulated radiation therapy, signal processing, image reconstruction and so on. In this paper, based on a new reformulation for the SFP, we propose a new halfspace-relaxation projection method for the SFP. The method is implemented very easily and is proven to be fully convergent to the solution for the case where the solution set of the SFP is nonempty. Preliminary computational experience is also reported. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：1218 / 1229

页数：12

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