  This paper presents a new approach for training artificial neural networks
using techniques for solving the constraint satisfaction problem (CSP). The
quotient gradient system (QGS) is a trajectory-based method for solving the
CSP. This study converts the training set of a neural network into a CSP and
uses the QGS to find its solutions. The QGS finds the global minimum of the
optimization problem by tracking trajectories of a nonlinear dynamical system
and does not stop at a local minimum of the optimization problem. Lyapunov
theory is used to prove the asymptotic stability of the solutions with and
without the presence of measurement errors. Numerical examples illustrate the
effectiveness of the proposed methodology and compare it to a genetic algorithm
and error backpropagation.
