Universal regularization methods: varying the power, the smoothness and the accuracy

Coralia Cartis, Nick I. Gould, Philippe L. Toint

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Adaptive cubic regularization methods have emerged as a credible alternative to linesearch and trust-region for smooth nonconvex optimization, with optimal complexity amongst second-order methods. Here we consider a general/new class of adaptive regularization methods that use first- or higher-order local Taylor models of the objective regularized by a(ny) power of the step size and applied to convexly constrained optimization problems. We investigate the worst-case evaluation complexity/global rate of convergence of these algorithms, when the level of sufficient smoothness of the objective may be unknown or may even be absent. We find that the methods accurately reflect in their complexity the degree of smoothness of the objective and satisfy increasingly better bounds with improving model accuracy. The bounds vary continuously and robustly with respect to the regularization power and accuracy of the model and the degree of smoothness of the objective.

langue originaleAnglais
Pages (de - à)595-615
Nombre de pages21
journalSIAM Journal on Optimization
Numéro de publication1
Les DOIs
Etat de la publicationPublié - 1 janv. 2019

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  • Oxford University

    Philippe Toint (Chercheur visiteur)

    20 nov. 20196 déc. 2019

    Activité: Types de Visite d'une organisation externeVisite à une institution académique externe

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