A Note About The Complexity Of Minimizing
           Nesterov's Smooth Chebyshev-Rosenbrock Function

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

This  short note  considers and  resolves the  apparent  contradiction between
known  worst-case complexity results  for first  and second-order  methods for
solving unconstrained smooth nonconvex optimization problems and a recent note
by Jarre (2011) implying a very  large lower bound on the number of iterations
required to  reach the  solution's neighbourhood for  a specific  problem with
variable dimension.

Keywords: evaluation complexity, worst-case analysis, nonconvex
          optimization.