Recurrent neural networks for solving linear inequalities and equations
Recurrent neural networks for solving linear inequalities and equations
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DOI：
10.1109/81.754846
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发表时间：
1999-04
影响因子：
5.1
通讯作者：
Youshen Xia;Jun Wang;Donald L. Hung
中科院分区：
文献类型：
--
作者：
Youshen Xia;Jun Wang;Donald L. Hung
提出了求解线性不等式和等式系统的两种递归神经网络：连续时间递归神经网络和离散时间递归神经网络。除了基本的连续时间和离散时间神经网络模型，两个改进的离散时间神经网络具有更快的收敛速度，通过使用缩放技术。所提出的神经网络可以解决线性不等式和等式系统，可以同时解决线性规划及其对偶，从而扩展和修改现有的神经网络求解线性方程组或不等式。给出了神经网络全局收敛性的严格证明。文中还讨论了递归神经网络的数字实现。
This paper presents two types of recurrent neural networks, continuous-time and discrete-time ones, for solving linear inequality and equality systems. In addition to the basic continuous-time and discrete-time neural-network models, two improved discrete-time neural networks with faster convergence rate are proposed by use of scaling techniques. The proposed neural networks can solve a linear inequality and equality system, can solve a linear program and its dual simultaneously, and thus extend and modify existing neural networks for solving linear equations or inequalities. Rigorous proofs on the global convergence of the proposed neural networks are given. Digital realization of the proposed recurrent neural networks are also discussed.