| 凸可行问题的块迭代次梯度投影算法 |
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| 引用本文： | 党亚峥,高岩,支丽平.凸可行问题的块迭代次梯度投影算法[J].运筹学学报,2011,15(1):59-70. |
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| 作者姓名： | 党亚峥 高岩 支丽平 |
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| 作者单位： | 1. 上海理工大学管理学院,上海,200093;河南理工大学,河南焦作,454000
2. 上海理工大学管理学院,上海,200093 |
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| 基金项目： | supported by National Science Foundation of China(under grant:10671126); Shanghai leading academic discipline project(under grant:S30501); the Innovation Fund Project for Graduate Student of Shanghai(JWCXSL1001); Youth Foundation of Henan Polytechnic University(Q2009-3); Applied Mathematics Provincial-level Key Discipline of Henan Province,Operations Research and Control Theory Key Discipline of Henan Polytechnic Univrsity |
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| 摘 要： | 本文,针对由非线性不等式系统构成的凸可行问题,提出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.将非线性不等式系统分成若干个子系统,然后将当前迭代点在子系统各个子集上的次梯度投影的凸组合作为当前迭代点在这个子系统上的近似投影.在较弱条件下证明了两种算法的收敛性.
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| 关 键 词： | 运筹学 凸函数 凸可行问题 次梯度 收敛性 |
Block-Iterative Subgradient Projection Algorithms for the Convex Feasibility Problem |
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| Dang Yazheng,Gao Yan,Zhi Liping.Block-Iterative Subgradient Projection Algorithms for the Convex Feasibility Problem[J].OR Transactions,2011,15(1):59-70. |
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| Authors: | Dang Yazheng Gao Yan Zhi Liping |
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| Institution: | Dang Yazheng Gao Yan Zhi Liping 1.School of Management,University of Shanghai for Science and Technology,Shanghai 200093,China,2.Henan Polytechnic University,Henan Jiaozuo 454000 |
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| Abstract: | In this paper,sequential block-iterative subgradient projection algorithm and parallel block-iterative subgradient projection algorithm for solving the convex feasibility problem expressed by the system of inequalities are presented. Each step in these methods consists of finding the approximation projection of the current point on the subsystem which is constructed through parting the system of inequalities into several blocks.The convergence for both of sequential block-iterative subgradient projection al... |
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| Keywords: | Operations research convex function convex feasibility problem subgradient convergence |
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