An example of slow convergence for Newton's method on a function with
  globally Lipschitz continuous Hessian

         C. Cartis, N. I. M. Gould and Ph. L. Toint

             Report NAXYS-03-2013      5th May 2013

Abstract.
An example is presented where Newton's method for unconstrained minimization
is applied to find an eps-approximate first-order critical point of a
smooth function and takes  a multiple of eps^{-2} iterations and
function evaluations to terminate, which is as many as the steepest-descent
method in its worst-case. The novel feature of the proposed example is that
the objective function has a globally Lipschitz-continuous Hessian, while a
previous example published by the same authors only ensured this critical
property along the path of iterates, which is impossible to verify a
priori.