Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/326270
Type: Artigo
Title: Worst-case Evaluation Complexity For Unconstrained Nonlinear Optimization Using High-order Regularized Models
Author: Birgin
E. G.; Gardenghi
J. L.; Martinez
J. M.; Santos
S. A.; Toint
Ph. L.
Abstract: The worst-case evaluation complexity for smooth (possibly nonconvex) unconstrained optimization is considered. It is shown that, if one is willing to use derivatives of the objective function up to order p (for p >= 1) and to assume Lipschitz continuity of the p-th derivative, then an epsilon-approximate first-order critical point can be computed in at most O(epsilon -((p+1)/p)) evaluations of the problem's objective function and its derivatives. This generalizes and subsumes results known for p = 1 and p = 2.
Subject: Nonlinear Optimization
Unconstrained Optimization
Evaluation Complexity
High-order Models
Regularization
Editor: Springer Heidelberg
Heidelberg
Rights: fechado
Identifier DOI: 10.1007/s10107-016-1065-8
Address: https://link-springer-com.ez88.periodicos.capes.gov.br/article/10.1007/s10107-016-1065-8
Date Issue: 2017
Appears in Collections:Unicamp - Artigos e Outros Documentos

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