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 | |
| état | Publié - 1 juin 2013 |
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A note about the complexity of minimizing Nesterov's smooth Chebyshev-Rosenbrock function. / Cartis, Coralia; Gould, Nicholas I M; Toint, Philippe L.
Dans: Optimization Methods and Software, Vol 28, Numéro 3, 01.06.2013, p. 451-457.Résultats de recherche: Contribution à un journal/une revue › Article
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
VL - 28
SP - 451
EP - 457
JO - Optimization Methods and Software
JF - Optimization Methods and Software
SN - 1055-6788
IS - 3
ER -