一个求解二阶锥变分不等式问题的神经网络  

A neural network for solving the second-order cone constrained variational inequality problems

作　　者：刘怡彤 穆学文 LIU Yi-Tong;MU Xue-Wen(School of Mathematics and Statistics,Xidian University,Xi'an 710126,China)

机构地区：[1]西安电子科技大学数学与统计学院,西安710126

出　　处：《四川大学学报（自然科学版）》2023年第1期6-12,共7页Journal of Sichuan University(Natural Science Edition)

基　　金：陕西省自然科学基金(2021JM-118,2021JM-396,2021JM-116)。

摘　　要：本文提出了一个神经网络算法,以求解二阶锥变分不等式(SOCCVI)问题.该算法利用一个光滑化Fischer-Burmeister(FB)函数处理问题对应的KKT条件,将其转化为一个无约束优化问题.利用Lyapunov方法本文证明,在给定的条件下,该神经网络Lyapunov稳定,渐近稳定且指数稳定.数值模拟验证了该神经网络的运算效果.A neural network is proposed to solve the second-order cone constrained variational inequality(SOCCVI)problems.In this method,a smoothed Fischer-Burmeister(FB)function is used to deal with the KKT conditions corresponding to the problem,and then the KKT conditions are further transformed to an unconstrained optimization problem.The Lyapunov method is applied to show the Lyapunov stability,asymptotic stability and exponential stability of the neural network under given conditions.The effectiveness of the neural network is verified by numerical experiment.

关 键 词：神经网络 二阶锥 FISCHER-BURMEISTER函数 Lyapunov稳定 

分 类 号：O224[理学—运筹学与控制论]