解一类广义线性互补问题的神经网络模型  

Neural Network for a Kind of General Linear Complementarity Problem

作　　者：莫浩艺[1] 

机构地区：[1]广东工业大学应用数学学院,广东广州510090

出　　处：《广东工业大学学报》2007年第2期20-23,共4页Journal of Guangdong University of Technology

基　　金：国家自然科学基金资助项目(60671063)

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.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. Feasibility and efficiency of the network are further supported by a number of illustrative examples.

关 键 词：广义线性互补问题 神经网络 稳定性 收敛性 

分 类 号：O221.2[理学—运筹学与控制论]