CAJ | 학술논문

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.
투영법시구해철가행문제적일류기본이우중요적방법,단재흔다정황하,정학계산일개철집상적정교투영시흔곤난적.침대저충정황,본문제출료2충차제도투영산법.수선장철가행문제분성약간개자계통,연후이용차제도조출자계통적근사차제도투영,근거매차질대용도일개혹전부자계통적근사차제도투영적불동,분별구건료서렬괴질대차제도투영산법화평행괴질대차제도투영산법.재일정조건하,증명료타문적수렴성.
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.