| Minimax神经网络收敛性分析 |
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| 引用本文： | 叶仲泉,张邦礼.Minimax神经网络收敛性分析[J].信息与控制,1997,26(1):1-6. |
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| 作者姓名： | 叶仲泉 张邦礼 |
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| 作者单位： | 重庆大学应用数学系，重庆大学自动化系 |
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| 摘 要： | ｍｉｎｉｍａｘ问题的研究不仅在对策论、数学规划和最优控制中具有重要意义，而且许多类型的问题都需要寻求ｍｉｎｉｍａｘ问题的数值解．本文建立了连续动力系统神经网络来探讨ｍｉｎ－ｉｍａｘ问题，在适当的条件下利用Ｌｙａｐｕｎｏｖ函数讨论了网络的稳定性和收敛性，并证明了神经网络的稳定平衡点即为ｍｉｎｉｍａｘ问题的鞍点．这样的网络可由ＶＬＳＩ技术实现，且具有实时动力学行为，它们也很象生物处理的动力学．在适当的条件下，利用Ｌｙａｐｕｎｏｖ函数稳定性理论证明了该网络是Ｌｙａｐｕｎｏｖ稳定的，且网络收敛于鞍函数的鞍点
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| 关 键 词： | minimax问题，鞍函数，鞍点，连续动力系统神经网络，收敛性，Lyapunov函数 |
CONVERGENCE ANALYSIS ON MINIMAX NEURAL NETWORKS |
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| YE Zhongquan,ZHANG Bangli,CAO Changxiu.CONVERGENCE ANALYSIS ON MINIMAX NEURAL NETWORKS[J].Information and Control,1997,26(1):1-6. |
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| Authors: | YE Zhongquan ZHANG Bangli CAO Changxiu |
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| Affiliation: | *YE Zhongquan ** ZHANG Bangli ** CAO Changxiu * |
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| Abstract: | The study of the minimax problem is of important significance for the game theory,mathematical programming and optimal control,and numerical methods of solving these problems are needed in a wide class of applications.In this paper we construct a neural network of continuous time dynamical system to explore the minimax problem.The stability and convergence of the network are investigated by using Lyapunov function under suitable conditions.We have also proved that the equilibrium points of the network are the saddle points of the problem. |
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| Keywords: | minimax problem saddle function saddle points neural networks of continuous time dynamical system convergence Lyapunov function |
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