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Résumé
An adaptive regularization algorithm using highorder models is proposed for solving partially separable convexly constrained nonlinear optimization problems whose objective function contains nonLipschitzian 'qnorm regularization terms for q ϵ (0; 1). It is shown that the algorithm using a pthorder Taylor model for p odd needs in general at most O(ϵ ^{(p+1)=p}) evaluations of the objective function and its derivatives (at points where they are defined) to produce an ϵapproximate firstorder critical point. This result is obtained either with Taylor models, at the price of requiring the feasible set to be kernel centered" (which includes bound constraints and many other cases of interest), or with nonLipschitz models, at the price of passing the difficulty to the computation of the step. Since this complexity bound is identical in order to that already known for purely Lipschitzian minimization subject to convex constraints [C. Cartis, N. I. M. Gould, and Ph. L. Toint, IMA J. Numer. Anal., 32 (2012), pp. 16621695], the new result shows that introducing nonLipschitzian singularities in the objective function may not affect the worstcase evaluation complexity order. The result also shows that using the problem's partially separable structure (if present) does not affect the complexity order either. A final (worse) complexity bound is derived for the case where Taylor models are used with a general convex feasible set.
langue originale  Anglais 

Pages (de  à)  874903 
Nombre de pages  30 
journal  SIAM Journal on Optimization 
Volume  29 
Numéro de publication  1 
Les DOIs  
Etat de la publication  Publié  15 avr. 2019 
Empreinte digitale
Examiner les sujets de recherche de « Complexity of partially separable convexly constrained optimization with nonLipschitzian singularities ». Ensemble, ils forment une empreinte digitale unique.Projets
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