An ε-approximation approach for global optimization with an application to neural networks

This paper proposes an ε-approximation approach based on the tunneling methods for finding a globally optimal solution of a function of several variables. In this approach, after some locally minimal solution is found, one must obtain a new initial point from which a better local solution can be obtained by a gradient method. For that, a Newton-like method called the restoration procedure is used. Computational results of several standard test problems are presented. Further more, an application to hierarchical neural networks is discussed. Global optimization is an unavoidable task for optimizing a neural network, since a hierarchical neural network with repeated nonlinear mapping has generally many local minima with respect to weighting coefficients