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

Coralia Cartis, Nicholas I M Gould, Philippe L. Toint

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Résumé

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.

langue originaleAnglais
Pages (de - à)451-457
Nombre de pages7
journalOptimization Methods and Software
Volume28
Numéro de publication3
Les DOIs
Etat de la publicationPublié - 1 juin 2013

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