On the oracle complexity of first-order and derivative-free algorithms for smooth nonconvex minimization

Coralia Cartis, N.I.M. Gould, Philippe Toint

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Résumé

The (optimal) function/gradient evaluations worst-case complexity analysis available for the adaptive regularization algorithms with cubics (ARC) for nonconvex smooth unconstrained optimization is extended to finite-difference versions of this algorithm, yielding complexity bounds for first-order and derivative-free methods applied on the same problem class. A comparison with the results obtained for derivative-free methods by Vicente [Worst Case Complexity of Direct Search, Technical report, Preprint 10-17, Department of Mathematics, University of Coimbra, Coimbra, Portugal, 2010] is also discussed, giving some theoretical insight into the relative merits of various methods in this popular class of algorithms. © 2012 Society for Industrial and Applied Mathematics.
langue originaleAnglais
Pages (de - à)66-86
Nombre de pages21
journalSIAM Journal on Optimization
Volume22
Numéro de publication1
Les DOIs
Etat de la publicationPublié - 1 janv. 2012

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