Global Exponential Stability of a Neural Network for Inverse Variational Inequalities
Global Exponential Stability of a Neural Network for Inverse Variational Inequalities
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DOI：
10.1007/s10957-021-01915-x
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发表时间：
2021-08
影响因子：
1.9
通讯作者：
P. Vuong;Xiaozheng He;Duong Viet Thong
中科院分区：
文献类型：
--
作者：
P. Vuong;Xiaozheng He;Duong Viet Thong
我们研究了用于求解逆变分不等式的投影神经网络的收敛特性。在标准假设下，我们建立了所提出的神经网络的指数稳定性。考虑了所提出的神经网络的离散版本，从而产生了一种用于求解逆变分不等式的新投影方法，为此我们获得了线性收敛。我们通过考虑交通科学中出现的道路定价问题的应用来说明所提出的神经网络的有效性及其显式离散化。本文获得的结果为最近的一个悬而未决的问题提供了积极的答案，并改进了文献中的一些最新结果。
We investigate the convergence properties of a projected neural network for solving inverse variational inequalities. Under standard assumptions, we establish the exponential stability of the proposed neural network. A discrete version of the proposed neural network is considered, leading to a new projection method for solving inverse variational inequalities, for which we obtain the linear convergence. We illustrate the effectiveness of the proposed neural network and its explicit discretization by considering applications in the road pricing problem arising in transportation science. The results obtained in this paper provide a positive answer to a recent open question and improve several recent results in the literature.