| 实时求解线性规划问题的原对偶神经网络(英文) |
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| 引用本文： | 张雨浓,易称福,马伟木.实时求解线性规划问题的原对偶神经网络(英文)[J].运筹学学报,2010,14(3):1-10. |
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| 作者姓名： | 张雨浓 易称福 马伟木 |
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| 作者单位： | 1. 华南理工大学数学学院, 广州 510641;2. 北京大学北京国际数学研究中心, 北京 100871 |
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| 基金项目： | funded by National Science Foundation of China under Grant 60775050; by the Science and Technology Office of Sun Yat-Sen University(SYSU) |
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| 摘 要： | 本文探讨了线性规划的原问题与对偶问题理论,并在此基础上可开发出一种用于在线求解线性规划的递归神经网络和应用于冗余机器手臂逆运动学的求解问题上.如,Tang等人开展的原对偶神经网络.但鉴于对偶理论的复杂性和多样性,该原对偶神经网络模型仅可以得到线性规划问题的可行解,而本文对该网络模型改进后可得到线性规划问题的最优解.仿真结果证实了这种改进模型在解决线性规划问题上的有效性、正确性和高效率.
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| 关 键 词： | 低秩稀疏矩阵优化 凸松弛模型 因子分解模型 精确恢复条件 收敛性 |
| 收稿时间： | 2020-03-30 |
On a Primal-Dual Neural Network for Online |
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| Zhang Yunong,Yi Chenfu,Ma Weimu.On a Primal-Dual Neural Network for Online[J].OR Transactions,2010,14(3):1-10. |
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| Authors: | Zhang Yunong Yi Chenfu Ma Weimu |
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| Institution: | 1. School of Mathematics, South China University of Technology, Guangzhou 510641, China;2. Beijing International Center For Mathematical Research, Peking University, Beijing 100871, China |
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| Abstract: | This paper investigates the theory of primal linear-programming (LP) problem and its dual problems, which could be used to develop a kind of recurrent neural network for solving online LP problems as well as kinematic control of redundant manipulators. For example, a so-called usual primal-dual neural network (PDNN) initiated by Tang et al. However, due to the complexity and diversity of duality theory, that PDNN needs to be improved so as to obtain the optimal solution(s) instead of feasible solutions. Computer-simulation results substantiate the efficacy and correctness of the improved PDNN model for online solution of LP problems. |
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| Keywords: | Primal and Dual Problems Neural Network Energy Function Optimal Solutions |
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