Minimax神经网络收敛性分析

CONVERGENCE ANALYSIS ON MINIMAX NEURAL NETWORKS

摘要: minimax问题的研究不仅在对策论、数学规划和最优控制中具有重要意义，而且许多类型的问题都需要寻求minimax问题的数值解。本文建立了连续动力系统神经网络来探讨min-imax问题，在适当的条件下利用Lyapunov函数讨论了网络的稳定性和收敛性，并证明了神经网络的稳定平衡点即为minimax问题的鞍点。这样的网络可由VLSI技术实现，且具有实时动力学行为，它们也很象生物处理的动力学。在适当的条件下，利用Lyapunov函数稳定性理论证明了该网络是Lyapunov稳定的，且网络收敛于鞍函数的鞍点．

Abstract: The study of the minimax problem is of important significance for the game theory,mathematical programming and optimal control,and numerical methods of solving these problems are needed in a wide class of applications.In this paper we construct a neural network of continuous-time dynamical system to explore the minimax problem.The stability and convergence of the network are investigated by using Lyapunov function under suitable conditions.We have also proved that the equilibrium points of the network are the saddle points of the problem.