A new halfspace-relaxation projection method for the split feasibility problem
A new halfspace-relaxation projection method for the split feasibility problem
复制标题
一种解决分割可行性问题的半空间松弛投影新方法
DOI：
10.1016/j.laa.2007.03.002
复制
发表时间：
2008-03-01
影响因子：
1.1
通讯作者：
Xiu, Naihua
中科院分区：
文献类型：
--
作者：
Qu, Biao;Xiu, Naihua
设C和Q分别是Rn和Rm中的非空闭凸集，A是m × n真实的矩阵.如果x存在，则求x是C的一个元素且Ax是Q的一个元素的问题称为分裂可行性问题（SFP）。该问题在调强放射治疗、信号处理、图像重建等领域具有重要意义，本文在对SFP进行新的重构的基础上，提出了一种新的SFP的半空间松弛投影方法。该方法是非常容易实现的，并被证明是完全收敛的解决方案的情况下，SFP的解决方案是非空的。初步的计算经验也报告。(C)2007爱思唯尔公司All rights reserved.
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.