解一类广义线性互补问题的神经网络模型

广东工业大学学报 ›› 2007, Vol. 24 ›› Issue (2): 20-23.

解一类广义线性互补问题的神经网络模型

广东工业大学应用数学学院广东广州510090；

出版日期:2007-07-02 发布日期:2007-07-02
基金资助:
国家自然科学基金资助项目(60671063)

Neural Network for a Kind of General Linear Complementarity Problem

(Faculty of Applied Mathematics,Guangdong University of Technology,Guangzhou 510090,China)

Online:2007-07-02 Published:2007-07-02

摘要/Abstract

摘要： 给出求解一类广义线性互补问题的一个非梯度的神经网络模型.运用Lyapunov稳定性理论和LaSalle不变集原理严格证明,当矩阵M半正定时,网络渐近稳定地收敛于原问题的一个精确解.该模型可以求解线性互补问题,它比已有模型简单,而且,它包括了求解二次优化问题的网络模型.数值模拟表明网络不仅可行而且有效.

关键词: 广义线性互补问题；神经网络；稳定性；收敛性；

Abstract: A nongradient neural network is presented for solving a kind of the general linear complementarity problem.With the Lyapunov theorem and LaSalle invariant set principle,the network is proved to be Lyapunov stable and globally convergent to an exact solution of the problem when the matrix M is positive semidefinite.The network can be used to solve the linear complementarity prlblem,and it is simpler than the existing network.Moreover,it includes the network of quadratic optimization problem.Feasi...

Key words: general linear complementarity problem； neural network； stability； convergence；

莫浩艺； . 解一类广义线性互补问题的神经网络模型[J]. 广东工业大学学报, 2007, 24(2): 20-23.

MO Hao-yi . Neural Network for a Kind of General Linear Complementarity Problem[J]. Journal of Guangdong University of Technology, 2007, 24(2): 20-23.

参考文献

[1] 夏又生,黄俊良. 一类线性互补问题的神经网络求解[J]. 东南大学学报. 1995(06)

[2] 高兴宝. 两类典型非线性问题的计算方法研究[D]. 西安电子科技大学 2000

[3] L. Fernandes,A. Friedlander,M. Guedes,J. Júdice. Solution of a General Linear Complementarity Problem Using Smooth Optimization and Its Application to Bilinear Programming and LCP[J] ,2001

[4] Xia Y S,Wang J.A general methodology for designing glob-ally convergent optimization neural networks. IEEETrans.Networks . 1998

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