广义射影神经网络的指数稳定性

研究了一类广义射影神经网络,分析了它的稳定性和收敛性.当映射和非对称时,分别定义了恰当的能量函数,在适当的条件下证明了该网络的全局收敛性和指数稳定性.与已有结果相比,文中的稳定性条件并不需要映射的可微性及映射和的对称性.理论分析和数值实例表明所得结果适用于非单调问题,而且给定的条件易于验证.由于该网络可求解一大类优化和平衡问题,因此文中结论具有一定的理论价值和实际意义.

Exponential stability of a general projection neural network

A general projection neural network is considered, and its stability and convergence are analyzed.When the sum of the underlying mappings is asymmetric,global convergence and exponential stability of the general projection neural network are strictly shown under mild conditions by defining the suitable energy functions,respectively.Compared with the existing results for this network,the given stability conditions do not require the differentiability of the mappings,and the symmetric of the sum of the mappings.Theoretical analysis and illustrative examples show that the obtained results can be applied to some non-monotone problems,and the given conditions can be easily checked.Since this network can be used to solve a broad class of optimization and equilibrium problems,the obtained results are significant in both theory and application.