A new neural network for nonlinear constrained optimization problems

Abstract

In this paper we introduce a new neural network for solving nonlinear constrained optimization problems. The energy function for the neural network with its neural dynamics is obtained from an application of the penalty-function method. We show that the system of the neural network is stable and an equilibrium point of the neural dynamics yields an optimal solution for the corresponding nonlinear constrained optimization problem. Based on the relationship between the equilibrium points and the energy function, an algorithm is developed for computing an equilibrium point of the system or an optimal solution to its optimization problem. The efficiency of the algorithm is demonstrated with several numerical examples. © Springer-Verlag 2004.