A note about the complexity of minimizing Nesterov's smooth Chebyshev-Rosenbrock function

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 [On Nesterov's smooth Chebyshev-Rosenbrock function, Optim. Methods Softw. (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. © 2013 Copyright Taylor and Francis Group, LLC.