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Machine Learning models incorporating multiple layered learning networks havebeen seen to provide effective models for various classification problems. Theresulting optimization problem to solve for the optimal vector minimizing theempirical risk is, however, highly nonlinear. This presents a challenge toapplication and development of appropriate optimization algorithms for solvingthe problem. In this paper, we summarize the primary challenges involved andpresent the case for a Newton-based method incorporating directions of negativecurvature, including promising numerical results on data arising from securityanomally deetection.

Algorithms for solving optimization problems arising from deep neural net models: smooth problems