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 revueArticle

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
étatPublié - 1 janv. 2017

Empreinte digitale

Constrained Optimization
Nonlinear Optimization
Critical point
First-order
Constrained optimization
Equality Constraints
Constrained Optimization Problem
Inequality Constraints
Homotopy
Objective function
Valid
Optimization
Evaluation

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On the complexity of finding first-order critical points in constrained nonlinear optimization : Corrigendum. / Cartis, C.; Gould, N. I.M.; Toint, Ph L.

Dans: Mathematical Programming, Vol 161, Numéro 1-2, 01.01.2017, p. 611-626.

Résultats de recherche: Contribution à un journal/une revueArticle

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AU - Cartis, C.

AU - Gould, N. I.M.

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