求解一类新的非线性变分不等式的神经网络  

A neural network for solving a new class of nonlinear variational inequalities

作　　者：毕红梅[1] 王婧[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安710062

出　　处：《重庆工商大学学报（自然科学版）》2007年第2期111-115,共5页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：国家自然科学基金(10571115)

摘　　要：考虑了一类新的非线性变分不等式,提出了求解的一个神经网络模型．在映射弱强制条件下,严格证明了该网络是Lyapunov稳定的,并且渐进收敛于原问题的一个精确解．此外,在适当的条件下证明了该模型的指数稳定性．数值实例表明该模型可行且有效．This paper considers a new class of nonlinear variational inequalities, and presents a new neuarl network to solve it. The proposed neural netwrk is shown to be stable in the sense of Lyapunov and to have a finite- time convergence under the weak casting coercivity condition. Meanwhile the exponential stability of the proposed network is also proved under mild conditions. The new model has simple structure and can be implemented in hardwar. The validity and transient behavior of the proposed neural network are demonstrated by several numerical examples.

关 键 词：变分不等式 神经网络 指数稳定性 有限时间收敛性 

分 类 号：O221.2[理学—运筹学与控制论]