一个解决线性互补问题的新型神经网络

A Novel Neural Network for Linear Complementarity Problems

中文关键词:  神经网络  线性互补  收敛性  稳定性.

英文关键词:neural network  linear complementarity  convergence  stability.

中文摘要:

      本文构造了一个新型的解决线性互补问题的神经网络.不同于那些运用罚函数和拉格朗日函数的神经网络,它的结构简单,易于计算.我们证明了该神经网络的全局收敛性和稳定性,并给出数值实验检验其有效性.

英文摘要:

      In this paper, we present a neural network for solving linear complementarity problem in real time. It possesses a very simple structure for implementation in hardware. In the theoretical aspect, this network is different from the existing networks which use the penalty functions or Lagrangians. We prove that the proposed neural network converges globally to the solution set of the problem starting from any initial point. In addition, the stability of the related differential equation system is analyzed and five numerical examples are given to verify the validity of the neural network.