基于分块矩阵的投影型神经网络收敛性分析*

投影神经网络算法被誉为最有希望解决优化问题的算法之一，可用于求解优化问题的前提是它应具有全局收敛性。根据凸二次规划约束条件的特点，利用常微分方程理论、M-矩阵理论，通过构造适当的Lyapunov函数，获得了该网络求解一类凸二次规划问题的全局指数收敛性条件，该条件只与神经元连接权矩阵的部分元素有关，其比现有文献所得的收敛条件更弱。最后给出一组实例，说明该网络计算上是可行和有效的。

Convergence analysis of projective neural networks based on partial matrix

Projective neural network is the most promising method for solving programming problems, but before it application in practice, neural system must be stable. Based on ordinary differential theory, M-matrix theory, and the character of activate function, by constructing appropriate Lyapunov functional, obtained some globally convergent conditions, this conditions were only relate to some elements of the weight matrix, they were more weaker than previous publications. It presented one simulation example to show the validity of the main results.