| 积空间中求解凸不等式系统的不完全投影算法 |
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| 引用本文： | 党亚峥,高岩.积空间中求解凸不等式系统的不完全投影算法[J].上海理工大学学报,2012,34(4):359-363. |
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| 作者姓名： | 党亚峥 高岩 |
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| 作者单位： | 1. 河南理工大学数学与信息科学学院,焦作,454001
2. 上海理工大学管理学院,上海,200093 |
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| 基金项目： | 国家自然科学基金资助项目，上海市重点学科建设资助项目，上海市科委资助项目，河南省教育自然科学基金资助项目 |
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| 摘 要： | 针对凸不等式系统提出了一种具有可变权参数和下松弛因子的平行不完全投影算法,经过有限次的投影算法得到不完全投影点,并且通过构造一个新的积空间,将欧氏空间中的平行不完全投影算法转化为新空间中的半序列不完全投影算法,使得平行的不完全投影法的收敛性由半序列不完全投影算法的收敛性证明直接得到,在一定程度上简化了平行不完全投影算法的收敛性证明.
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| 关 键 词： | 凸不等式系统 不完全投影算法 积空间 收敛性分析 |
Incomplete Projection Algorithm for Solving a System of Convex Inequalities in a Product Space |
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| DANG Ya zheng and GAO Yan.Incomplete Projection Algorithm for Solving a System of Convex Inequalities in a Product Space[J].Journal of University of Shanghai For Science and Technology,2012,34(4):359-363. |
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| Authors: | DANG Ya zheng and GAO Yan |
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| Institution: | 1.School of Mathematics and Information Science,Henan Polytechnic University,Jiaozuo 454001,China; 2.Business School,University of Shanghai for Science and Technology,Shanghai 200093,China) |
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| Abstract: | A parallel incomplete projection method with variable weights and under relaxation coefficient was proposed for the system of convex inequalities.Then,the parallel incomplete projection method was transformed in a given Euclidean space into a semi-sequential incomplete projection method in a product space by constructing a new space.Convergent results for the parallel incomplete projection methods may be obtained from the semi-sequential ones,which can simplify the proof of the convergence. |
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| Keywords: | convex inequalities system incomplete projection algorithm product space convergence analysis |
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