  This paper investigates the global convergence of stepsized Newton methods
for convex functions. We propose several simple stepsize schedules with fast
global convergence guarantees, up to $\mathcal{O} (k^{-3})$, nearly matching
lower complexity bounds $\Omega (k^{-3.5})$ of second-order methods. For cases
with multiple plausible smoothness parameterizations or an unknown smoothness
constant, we introduce a stepsize backtracking procedure that ensures
convergence as if the optimal smoothness parameters were known.
