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

Coralia Cartis (coralia.cartis***at***ed.ac.uk)
Nicholas I. M. Gould (nick.gould***at***sftc.ac.uk)
Philippe L. Toint (philippe.toint***at***fundp.ac.be)

Abstract: 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

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Citation: Technical Report naXys-20-2011, Namur Center for Complex Systems, University of Namur, Belgium

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Entry Submitted: 07/16/2011
Entry Accepted: 07/16/2011
Entry Last Modified: 08/30/2011

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