Newton Method Revisited: Global Convergence Rates up to $\mathcal{O}\left(k^{-3}\right)$ for Stepsize Schedules and Linesearch Procedures

Slavomír Hanzely, Farshed Abdukhakimov, Martin Takáč

This paper investigates the global convergence of stepsized Newton methods for convex functions with Hölder continuous Hessians or third derivatives. We propose several simple step…