一类变量变分不等式的神经网络

Neural networks for a class of variant variational inequalities

基于解的充分必要条件 ,讨论了一类变量变分不等式的神经网络方法 .针对问题的自身结构特点 ,分别给出了求解非线性问题的一个神经网络模型和线性问题的统一的神经网络模型 ,且模型均不含网络参数 .在适当的条件下 ,严格证明了它们是Lyapunov稳定的 ,并且大范围渐近收敛于原问题的精确解 .此外 ,还讨论了解线性问题的网络模型的全局指数稳定性 .

Neural networks for solving a class of variant variational inequalities are studied under the necessary and sufficient conditions of the solution. A neural network for the nonlinear problem and a unified neural network model for the linear problem are proposed by the inherent property of the problem. No network parameter is in the proposed models. They are proved to be Lyapunov stable and asymptotically convergent to an exact solution of the original problem in the large under proper conditions. Moreover, the globally exponential stability of the model for the linear problem is studied. Finally, the feasibility and efficiency of the proposed models are confirmed by numerical experiments.