解一类线性约束线性变分不等式的神经网络

摘要

A class of linearly constrained linear variational inequalities is considered.Two neural networks for solving it are proposed by transforming it into the equivalent equations.The proposed models are proved to be Liapunov stable and globally converge to an solution of the underlying problem.Moreover,the global exponential stability of the proposed models are shown under certain conditions.The size of each proposed models is the same as that of the underlying problems,and the network parameter is easy to be chosen.The feasibility and effectiveness of the proposed neural networks are supported by the simulation experiments.%研究了一类线性约束线性变分不等式问题.通过将其转化为等价的方程组,提出了求解它的两个神经网络模型.利用稳定性理论证明了新模型是Liapunov稳定的,并且全局收敛于原问题的一个精确解.此外,在一定的条件下证明了它们的全局指数稳定性.新模型的规模均与原问题相同,且参数易于选择,模拟实验表明它们可行有效.