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

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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 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

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10.1080/10556788.2012.722632

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1 Citations
6 Article
3 Papier 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

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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. (Co-investigateur), Gould, N. I. M. (Co-investigateur) & Cartis, C. (Co-investigateur)
1/11/08 → …
Projet: Recherche
ADALGOPT: ADALGOPT - Algorithmes avancés en optimisation non-linéaire
Sartenaer, A. (Co-investigateur) & Toint, P. (Co-investigateur)
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
Toint, P. (Orateur invité)
5 févr. 2016
Activité: Discours ou présentation › Présentation orale
How much patience do you have? Issues in complexity for nonlinear optimization
Toint, P. (Orateur)
31 janv. 2016
Activité: Discours ou présentation › Présentation orale
Hong Kong Polytechnic University
Toint, P. (Chercheur visiteur)
31 janv. 2016 → 14 févr. 2016
Activité: Visite d'une organisation externe › Recherche/Enseignement dans une institution externe

Leverhulme Fellow
Toint, P. (Bénéficiaire), sept. 2015
Prix: Bourse attribuée par concours

Contient cette citation

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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.",

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

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