Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients

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Résumé

The worst-case behaviour of a general class of regularization algorithms is considered in the case where only objective function values and associated gradient vectors are evaluated. Upper bounds are derived on the number of such evaluations that are needed for the algorithm to produce an approximate first-order critical point whose accuracy is within a user-defined threshold. The analysis covers the entire range of meaningful powers in the regularization term as well as in the Hölder exponent for the gradient. The resulting complexity bounds vary according to the regularization power and the assumed Hölder exponent, recovering known results when available.
langue originaleAnglais
Pages (de - à)1273-1298
Nombre de pages26
journalOptimization Methods and Software
Volume32
Numéro de publication6
Les DOIs
étatPublié - 2 nov. 2017

Empreinte digitale

Unconstrained Optimization
Regularization Method
Regularization
Gradient
Evaluation
Exponent
Gradient vector
Critical point
Objective function
Entire
Vary
Cover
Upper bound
First-order
Term
Range of data

Citer ceci

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Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients. / Toint, Philippe.

Dans: Optimization Methods and Software, Vol 32, Numéro 6, 02.11.2017, p. 1273-1298.

Résultats de recherche: Contribution à un journal/une revueArticle

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