Gradient Systems with Diffusively Coupled Many-Bodies for Optimization Problems and Their Realization by Neural Networks

Abstract

This paper presents dynamic models to search for optimum points by using gradient systems with diffusively coupled many-bodies, and indicates that the dynamic models for quadratic programming problems with variables constrained on the closed interval [0, 1]'s are realized by coupled neural network(N.N.) systems. Concretely, these are external types in which the outputs from neurons are coupled and internal types in which the inner variables of neurons are coupled. Computer simulation for simple problems are carried out to confirm the optimization ability of the proposed coupled N.N. models. In addition, the relation between the proposed internal types and time-dependent Ginzburg-Landau equation is indicated.