求解一类新的非线性变分不等式的神经网络

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．

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

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 fi- nite-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 imple- mented in hardwar.The validity and transient behavior of the proposed neural network are demonstrated by sever- al numerical examples.