Optimisation strategies for nonconvex functions and applications to neural networks

In this paper the authors describe some useful strategies for nonconvex optimisation in order to determine the global minimum of the error function of a Multi-Layer Perceptron. The proposed approach is founded on a new concept, called "non suspiciousness", which can be seen as a generalisation of convexity. Relations both with classical unconstrained optimisation results and with recent contributions in the field of supervised neural networks are examined. The preliminary numerical experiences show that the ideas behind the illustrated algorithm are interesting, although they require further investigation.