Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models

E. G. Birgin, J. L. Gardenghi, J. M. Martínez, S. A. Santos, P. L. Toint

Résultats de recherche: Contribution à un journal/une revueArticle

Résumé

The worst-case evaluation complexity for smooth (possibly nonconvex) unconstrained optimization is considered. It is shown that, if one is willing to use derivatives of the objective function up to order p (for p≥ 1 ) and to assume Lipschitz continuity of the p-th derivative, then an ϵ-approximate first-order critical point can be computed in at most O(ϵ - ( p + 1 ) / p) evaluations of the problem’s objective function and its derivatives. This generalizes and subsumes results known for p= 1 and p= 2.

langue originaleAnglais
Pages (de - à)359-368
Nombre de pages10
journalMathematical Programming
Volume163
Numéro de publication1-2
Les DOIs
étatPublié - 15 avr. 2017

Empreinte digitale

Unconstrained Optimization
Nonlinear Optimization
Higher Order
Derivatives
Derivative
Evaluation
Objective function
Lipschitz Continuity
Nonconvex Optimization
Critical point
Model
First-order
Generalise

Citer ceci

Birgin, E. G. ; Gardenghi, J. L. ; Martínez, J. M. ; Santos, S. A. ; Toint, P. L. / Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models. Dans: Mathematical Programming. 2017 ; Vol 163, Numéro 1-2. p. 359-368.
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Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models. / Birgin, E. G.; Gardenghi, J. L.; Martínez, J. M.; Santos, S. A.; Toint, P. L.

Dans: Mathematical Programming, Vol 163, Numéro 1-2, 15.04.2017, p. 359-368.

Résultats de recherche: Contribution à un journal/une revueArticle

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