Inexact Nonconvex Newton-Type Methods

The paper aims to extend the theory and application of nonconvex Newton-type methods, namely trust region cubic regularization, settings in which, addition solution subproblems, gradient Hessian objective function are approximated. Using certain conditions on such approximations, establishes optimal worst-case iteration complexities as exact counterparts. This is part a broader research program designing, analyzing, implementing efficient second-order optimization methods for large-scale machine learning applications. authors were based at UC Berkeley when idea project was conceived. first two PhD students, third author postdoc, all supervised by fourth author.