求解多集合分裂可行问题的不精确投影算法

Inexact Projection Methods for Solving Multiple- sets Split Feasibility Problem

文中基于求解分裂可行问题的不精确投影算法,推广到求解多集合分裂可行问题。首先,用到包含给定闭凸集的半空间上的投影代替原来到闭凸集上的投影,投影更容易计算。其次,用类-Armijo搜索获取步长代替恒定步长,并且利用得到的迭代步作为一个预测步,再进行一次校正,提出了预测校正不精确投影算法。该算法不需要计算矩阵的范数和最大特征值。文中还证明了预测校正算法的全局收敛性,最后给出了算法的数值实验结果,表明不精确投影算法是可行稳定的,且预测校正算法具有更快的收敛速度。

Based on the inexact projection-type method for solving the split feasibility problem, present the inexact projection methods to solve the multiple-sets split feasibility problem. Firstly ,each iteration of the first proposed algorithm consists of a projection onto a half- space which includes the given non-empty closed convex set. The new algorithm is easy to implement. Secondly, modification of the in- exact projection method is presented with constant stepsize by adopting Armijo-like searches which does not require the computation of the matrix norm and the largest eigenvalue, and make another correction by using iteration as a predicting step. It has also proved the glob- al convergence of the predictor-corrector algorithm, and given the numerical experiment results which show that the inexact projection al- gorithm is feasible and stable, the predictor-corrector algorithm has a faster convergence rate.