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

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

doi:10.1080/10556788.2012.722632

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

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

Namur Institute for Complex Systems

Résultats de recherche: Contribution à un journal/une revue › Article › Revue par des pairs

30 Téléchargements (Pure)

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 originale	Anglais
Pages (de - à)	451-457
Nombre de pages	7
journal	Optimization Methods and Software
Volume	28
Numéro de publication	3
Les DOIs	https://doi.org/10.1080/10556788.2012.722632
Etat de la publication	Publié - 1 juin 2013

Accès au document

10.1080/10556788.2012.722632

NTR 20 2011manuscrit soumis, 643 KB

Autres fichiers et liens

Link to publication in Scopus

1 Citations
6 Article
3 Article de travail
1 Livre
1 Chapitre

Evaluation complexity of algorithms for nonconvex optimization
Cartis, C., Gould, N. I. M. & TOINT, P., juil. 2022, SIAM. 600 p. (SIAM-MOS Series on Optimization)
Résultats de recherche: Livre/Rapport/Revue › Livre
Adaptive regularization algorithms with inexact evaluations for nonconvex optimization
Bellavia, S., Gurioli, G., Morini, B. & Toint, P., 2 janv. 2020, Dans: SIAM Journal on Optimization. 29, 4, p. 2881-2915 35 p.
Résultats de recherche: Contribution à un journal/une revue › Article › Revue par des pairs

Accès ouvert
File
37 Téléchargements (Pure)
Evaluation complexity bounds for smooth constrained nonlinear optimization using scaled KKT conditions and high-order models
Cartis, C., Gould, N. I. M. & Toint, P., juin 2019, Springer Optimization and Its Applications: Algorithms, Complexity and Applications. Demetriou, I. & Pardalos, P. (eds.). Springer Heidelberg, p. 5-26 22 p. (Springer Optimization and Its Applications; Vol 145).
Résultats de recherche: Contribution dans un livre/un catalogue/un rapport/dans les actes d'une conférence › Chapitre

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

Leverhulme Fellow
TOINT, Philippe (Bénéficiaire), sept. 2015
Prix: Bourse attribuée par concours

Contient cette citation

@article{53354db12c8843d8be7ec140b0c43392,

title = "A note about the complexity of minimizing Nesterov's smooth Chebyshev-Rosenbrock function",

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 [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.",

keywords = "evaluation complexity, nonconvex optimization, worst-case analysis",

author = "Coralia Cartis and Gould, {Nicholas I M} and Toint, {Philippe L.}",

year = "2013",

month = jun,

day = "1",

doi = "10.1080/10556788.2012.722632",

language = "English",

volume = "28",

pages = "451--457",

journal = "Optimization Methods and Software",

issn = "1055-6788",

publisher = "Taylor & Francis",

number = "3",

}

TY - JOUR

T1 - A note about the complexity of minimizing Nesterov's smooth Chebyshev-Rosenbrock function

AU - Cartis, Coralia

AU - Gould, Nicholas I M

AU - Toint, Philippe L.

PY - 2013/6/1

Y1 - 2013/6/1

N2 - 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.

AB - 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.

KW - evaluation complexity

KW - nonconvex optimization

KW - worst-case analysis

UR - http://www.scopus.com/inward/record.url?scp=84878316454&partnerID=8YFLogxK

U2 - 10.1080/10556788.2012.722632

DO - 10.1080/10556788.2012.722632

M3 - Article

AN - SCOPUS:84878316454

SN - 1055-6788

VL - 28

SP - 451

EP - 457

JO - Optimization Methods and Software

JF - Optimization Methods and Software

IS - 3

ER -

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

Résumé

Accès au document

Autres fichiers et liens

Empreinte digitale

Résultat de recherche

Projets

Activités

Prix

Contient cette citation