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

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

doi:10.1137/100812276

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 originale	Anglais
Pages (de - à)	66-86
Nombre de pages	21
journal	SIAM Journal on Optimization
Volume	22
Numéro de publication	1
Les DOIs	https://doi.org/10.1137/100812276
Etat de la publication	Publié - 1 janv. 2012

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2 Actif

Complexity in nonlinear optimization
TOINT, P., Gould, N. I. M. & Cartis, C.
1/11/08 → …
Projet: Recherche
ADALGOPT: ADALGOPT - Algorithmes avancés en optimisation non-linéaire
SARTENAER, A. & TOINT, P.
1/01/87 → …
Projet: Axe de recherche

3 Présentation orale
1 Recherche/Enseignement dans une institution externe
1 Visite à une institution académique externe

How much patience do you have? Issues in complexity for nonlinear optimization
Philippe Toint (Orateur invité)
5 févr. 2016
Activité: Types de discours ou de présentation › Présentation orale
Polytechnic University of Hong Kong
Philippe Toint (Chercheur visiteur)
31 janv. 2016 → 14 févr. 2016
Activité: Types de Visite d'une organisation externe › Recherche/Enseignement dans une institution externe
How much patience do you have? Issues in complexity for nonlinear optimization
Philippe Toint (Orateur)
31 janv. 2016
Activité: Types de discours ou de présentation › Présentation orale

Contient cette citation

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

abstract = "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. {\textcopyright} 2012 Society for Industrial and Applied Mathematics.",

keywords = " nonconvex optimization., finite-differences, oracle complexity, first-order methods, worst-case analysis, derivative free optimization",

author = "Coralia Cartis and N.I.M. Gould and Philippe Toint",

note = "Publication code : FP SB092/2010/03 ; SB04977/2010/03",

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doi = "10.1137/100812276",

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

Résumé

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Autres fichiers et liens

Complexity in nonlinear optimization

ADALGOPT: ADALGOPT - Algorithmes avancés en optimisation non-linéaire

How much patience do you have? Issues in complexity for nonlinear optimization

Polytechnic University of Hong Kong

How much patience do you have? Issues in complexity for nonlinear optimization

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