Global exponential stability of neural networks with globally Lipschitz continuous activations and its application to linear variational inequality problem.

Global exponential stability of neural networks with globally Lipschitz continuous activations and its application to linear variational inequality problem. Research Abstract Details 

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Global exponential stability of neural networks with globally Lipschitz continuous activations and its application to linear variational inequality problem. Abstract Text:

X B Liang,J Si,

This paper investigates the existence, uniqueness, and global exponential stability (GES) of the equilibrium point for a large class of neural networks with globally Lipschitz continuous activations including the widely used sigmoidal activations and the piecewise linear activations. The provided sufficient condition for GES is mild and some conditions easily examined in practice are also presented. The GES of neural networks in the case of locally Lipschitz continuous activations is also obtained under an appropriate condition. The analysis results given in the paper extend substantially the existing relevant stability results in the literature, and therefore expand significantly the application range of neural networks in solving optimization problems. As a demonstration, we apply the obtained analysis results to the design of a recurrent neural network (RNN) for solving the linear variational inequality problem (VIP) defined on any nonempty and closed box set, which includes the box constrained quadratic programming and the linear complementarity problem as the special cases. It can be inferred that the linear VIP has a unique solution for the class of Lyapunov diagonally stable matrices, and that the synthesized RNN is globally exponentially convergent to the unique solution. Some illustrative simulation examples are also given.

Global exponential stability of neural networks with globally Lipschitz continuous activations and its application to linear variational inequality problem. Publishing Authors By Initials

XB Liang,J Si,

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Global exponential stability of neural networks with globally Lipschitz continuous activations and its application to linear variational inequality problem. Journal Published:

PUBLICATION TYPE: Journal Article

Journal: IEEE transactions on neural networks / a publicati

VOLUME: 12

Page Numbers: 349-59

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ISSN: 1045-9227

DAY: 4

MONTH: 02

YEAR: 2001

Global exponential stability of neural networks with globally Lipschitz continuous activations and its application to linear variational inequality problem. Information

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LANGUAGE: eng

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Grant and Affiliation Information for Global exponential stability of neural networks with globally Lipschitz continuous activations and its application to linear variational inequality problem.

AFFILIATION: Dept. of Electr. and Comput. Eng., Delaware Univ., Newark, DE.

Country: United States

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MEDLINETA: IEEE Trans Neural Netw

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