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Résumé
An adaptive regularization algorithm is proposed that uses Taylor models of the objective of order p, (Formula presented.), of the unconstrained objective function, and that is guaranteed to find a first and secondorder critical point in at most (Formula presented.) function and derivatives evaluations, where ε _{1} and ε _{1} are prescribed first and secondorder optimality tolerances. This is a simple algorithm and associated analysis compared to the much more general approach in Cartis et al. [Sharp worstcase evaluation complexity bounds for arbitraryorder nonconvex optimization with inexpensive constraints, arXiv:1811.01220, 2018] that addresses the complexity of criticality higherthan two; here, we use standard optimality conditions and practical subproblem solves to show a sameorder sharp complexity bound for secondorder criticality. Our approach also extends the method in Birgin et al. [Worstcase evaluation complexity for unconstrained nonlinear optimization using highorder regularized models, Math. Prog. A 163(1) (2017), pp. 359–368] to finding secondorder critical points, under the same problem smoothness assumptions as were needed for firstorder complexity.
langue originale  Anglais 

Pages (de  à)  243256 
Nombre de pages  14 
journal  Optimization Methods and Software 
Volume  35 
Numéro de publication  2 
Les DOIs  
Etat de la publication  Publié  3 mars 2020 
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Projets
 2 Actif

Complexity in nonlinear optimization
TOINT, P., Gould, N. I. M. & Cartis, C.
1/11/08 → …
Projet: Recherche

ADALGOPT: ADALGOPT  Algorithmes avancés en optimisation nonlinéaire
1/01/87 → …
Projet: Axe de recherche
Activités
 1 Discours invité

Recent results in worstcase evaluation complexity for smooth and nonsmooth, exact and inexact, nonconvex optimization
Philippe TOINT (Orateur)
8 mai 2020Activité: Types de discours ou de présentation › Discours invité