A Model Solving Constrained Optimization Problem Based on the Stability of Hopfield Neural Network

Abstract

A neural network model is presented to solve the problem of generalized constrained optimization. The model is based on the stability criteria of Hopfield neural network. The energy function evaluating the stability of Hopfield neural network must be monotonously decreasing and bounded. By introducing Lagrange multiplier as constrained nerve cell and auxiliary variable as slack nerve cell, we constructed the neural network model, which has been proved to be stable and has a stable equilibrium point. The optimum solution of the system can be obtained by getting the equilibrium point of the model. In this way, a new approach is provided to solve the problem of constrained optimization system. Simulation shows that the neural network is effective in solving the constrained optimization problem