On the complexity of finding first-order critical points in constrained nonlinear optimization: Corrigendum

C. Cartis, N. I.M. Gould, Ph L. Toint

    Résultats de recherche: Contribution à un journal/une revueArticleRevue par des pairs

    Résumé

    The complexity of finding ϵ ϵ -approximate first-order critical points for the general smooth constrained optimization problem is shown to be no worse that O(ϵ −2 ) O(ϵ−2) in terms of function and constraints evaluations. This result is obtained by analyzing the worst-case behaviour of a first-order short-step homotopy algorithm consisting of a feasibility phase followed by an optimization phase, and requires minimal assumptions on the objective function. Since a bound of the same order is known to be valid for the unconstrained case, this leads to the conclusion that the presence of possibly nonlinear/nonconvex inequality/equality constraints is irrelevant for this bound to apply.

    langue originaleAnglais
    Pages (de - à)611-626
    Nombre de pages16
    journalMathematical Programming
    Volume161
    Numéro de publication1-2
    Les DOIs
    Etat de la publicationPublié - 1 janv. 2017

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