A Finite Newton Method for Classification Problems

A fundamental classification problem of data mining and machine learning is that of minimizing a strongly convex, piecewise quadratic function on the n-dimensional real space Rn. We show finite termination of a Newton method to the unique global solution starting from any point in Rn. If the function is well conditioned, then no stepsize is required from the start, and if not, an Armijo stepsize is used. In either case finite termination is guaranteed to the unique global minimum solution.