A Finite Newton Method for Classi cation Problems

Abstract

A fundamental classi cation 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 nite 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 nite termination is guaranteed to the unique global minimum solution.