Realization of Minimization Models with Higher Order Differential Equations by the Multi-Layered and Feedback Neural Networks

Abstract

Various types of trajectory techniques were considered in order to find the global minimum by means of the numerical integration of a differential equation. As new one of such techniques, the trajectory technique based on the higher order differential equation model is presented for continuous optimization problems with variables constrained on the closed interval _??_0, 1_??_. In order to realize the new differential equation model in neural networks, the new type of neural networks with the multi-layered and feedback structure is proposed. Simulation results for the neural networks based on the second and the third order differential equation models show global convergence.