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| 凸可行问题的块迭代次梯度投影算法 | |
| 引用本文： | 党亚峥,薛中会,高岩.凸可行问题的块迭代次梯度投影算法[J].河南理工大学学报(自然科学版),2012,31(1):116-120. |
| 作者姓名： | 党亚峥 薛中会 高岩 |
| 作者单位： | 1. 河南理工大学物理化学学院,河南焦作454000／上海理工大学管理学院,上海200093 2. 河南理工大学物理化学学院,河南焦作,454000 3. 上海理工大学管理学院,上海,200093 |
| 基金项目： | 国家自然科学基金项目，河南理工大学青年基金 |
| 摘 要： | 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. |
| 关 键 词： | 块迭代 次梯度 收敛性 凸可行问题 |
Block-iterative subgradient projection algorithm for the convex feasibility problem |
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| DANG Ya-zheng,XUE Zhong-hui,GAO Yan.Block-iterative subgradient projection algorithm for the convex feasibility problem[J].JOURNAL OF HENAN POLYTECHNIC UNIVERSITY,2012,31(1):116-120. | |
| Authors: | DANG Ya-zheng XUE Zhong-hui GAO Yan |
| Affiliation: | 1.School of Physicsand chemistry,Henan Polytechnic Univerity,Jiaozuo 454000,Henan,China;2.Business School,Shanghai Polytechnic University,Shanghai 200093,China) |
| Abstract: | 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. |
| Keywords: | block-iterative subgradient convergence convex feasibility problem |
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