知识与财富的链接
投影法是求解凸可行问题的一类基本而又重要的方法,但在很多情况下,精确计算一个凸集上的正交投影是很困难的.针对这种情况,本文提出了2种次梯度投影算法.首先将凸可行问题分成若干个子系统,然后利用次梯度找出子系统的近似次梯度投影,根据每次迭代用到一个或全部子系统的近似次梯度投影的不同,分别构建了序列块迭代次梯度投影算法和平行块迭代次梯度投影算法.在一定条件下,证明了它们的收敛性.
Projection algorithm is a general and important method for solving the convex feasibility problem,while in many cases,it is difficult to compute exactly the orthogonal projection.To address this situation,we present two kinds of subgradient projection methods for solving the convex feasibility problem in this paper.Firstly,part the nonlinear system into some subsystems;then construct the approximation projection of the subsystem by the convex combination of the subgradient projections on sets of the subsystem;next,iteration is generated either by sequential block-iterative subgradient projection or by parallel block-iterative subgradient projection,and under some conditions show their convergences.