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Résumé
A trustregion algorithm is presented for finding approximate minimizers of smooth unconstrained functions whose values and derivatives are subject to random noise. It is shown that, under suitable probabilistic assumptions, the new method finds (in expectation) an epsilonapproximate minimizer of arbitrary order q>0in at most O(epsilon^{(q+1)}) inexact evaluations of the function and its derivatives, providing the first such result for general optimality orders. The impact of intrinsic noise limiting the validity of the assumptions is also discussed and it is shown that difficulties are unlikely to occur in the firstorder version of the algorithm for sufficiently large gradients. Conversely, should these assumptions fail for specific realizations, then ``degraded'' optimality guarantees are shown to hold when failure occurs. These conclusions are then discussed and illustrated in the context of subsampling methods for finitesum optimization.
langue originale  Anglais 

Éditeur  Arxiv 
Volume  2112.06176 
Etat de la publication  Publié  2021 
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Examiner les sujets de recherche de « Trustregion algorithms: probabilistic complexity and intrinsic noise with applications to subsampling techniques ». Ensemble, ils forment une empreinte digitale unique.Activités
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DIEF, University of Florence
Philippe Toint (Chercheur visiteur)
20 sept. 2021 → 20 oct. 2021Activité: Types de Visite d'une organisation externe › Visite à une institution académique externe