解广义变分不等式的神经网络

A Neural Network for Solving General Variational Inequality Problems

考虑了广义变分不等式问题,基于解的充要条件,提出了求解它的一个神经网络模型。定义了恰当的能量函数,在适当的条件下证明了新模型是Lyapunov稳定的,并且收敛于原问题的一个精确解。此外,还证明了新模型的指数稳定性。新模型结构简单,易于硬件实现。数值实验表明,该模型不仅可行,而且有效。

This paper considers the general variational inequality problems. Based on the necessary and sufficient conditions of the solution, we proposed a new neural network to solve it. The proposed neural network is shown to be globally convergent, globally asvmptitically stable and glabally exponentially stable under mild conditions. The new model has simple structure and can be implemented in hardware. Simulation results demonstrate the effectiveness and characteristics of the proposed neural network.