Strong Evaluation Complexity of An Inexact Trust-Region Algorithm with for Arbitrary-Order Unconstrained Nonconvex Optimization

Coralia Cartis, Nicholas Ian Mark Gould, Philippe TOINT

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Résumé

A trust-region algorithm using inexact function and derivatives values is introduced for solving unconstrained smooth optimization problems. This algorithm uses high-order Taylor models and allows the search of strong approximate minimizers of arbitrary order. The evaluation complexity of finding a q-th approximate minimizer using this algorithm is then shown, under standard conditions, to be O( min_{j in{1,...,q}} epsilon_j^{-(q+1)} ) where the
\epsilon_j are the order-dependent requested accuracy thresholds. Remarkably, this order is identical to that of classical trust-region methods using exact information.
langue originaleAnglais
ÉditeurArxiv
Volume2011.00854
Etat de la publicationPublié - 5 nov. 2020

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