  Machine Learning models incorporating multiple layered learning networks have
been seen to provide effective models for various classification problems. The
resulting optimization problem to solve for the optimal vector minimizing the
empirical risk is, however, highly nonlinear. This presents a challenge to
application and development of appropriate optimization algorithms for solving
the problem. In this paper, we summarize the primary challenges involved and
present the case for a Newton-based method incorporating directions of negative
curvature, including promising numerical results on data arising from security
anomally deetection.
