求解超定线性方程组L_1─范数最优解的神经网络方法

A Neural Network Approach for Linear Absolute Value Problems

基于线性规划对偶理论，本文给出一种求解超定线性方程组Ｌ１─范数解的神经网络方法。这一方法由两部分组成，首先利用ＬＳＳＭ神经网络求出Ｌ１问题的近似对偶解，然后利用改进的Ｔ－Ｈ网络求Ｌ１─问题的解，当参数选择适当时，Ｔ－Ｈ网络的全局渐近稳定点就是问题的精确解，模拟试验也表明了这一方法的可行性。

Based on duality theory of linear programming,a neural network approach for least absolute value problems is proposed in this paper.The approach consists of two phases,at first.an approximate duality solution is obtained by using LSSM neural network,then the prime solution is given by using T-H neural network.It is demonstrated that the asymptotically stable point of T-H networkis the exact prime solution. Simulation results are given to show the validity of the proposed neural network approach.