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

Coralia Cartis, Nicholas I M Gould, Philippe L. Toint

Résultats de recherche: Contribution à un journal/une revueArticle

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Résumé

The complexity of finding e-Approximate first-order critical points for the general smooth constrained optimization problem is shown to be no worse that O(e-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. © 2012 Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society.

langue originaleAnglais
Pages (de - à)93-106
Nombre de pages14
journalMathematical Programming
Volume144
Numéro de publication1-2
Les DOIs
étatPublié - 2014

Empreinte digitale

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

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abstract = "The complexity of finding e-Approximate first-order critical points for the general smooth constrained optimization problem is shown to be no worse that O(e-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. {\circledC} 2012 Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society.",
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On the complexity of finding first-order critical points in constrained nonlinear optimization. / Cartis, Coralia; Gould, Nicholas I M; Toint, Philippe L.

Dans: Mathematical Programming, Vol 144, Numéro 1-2, 2014, p. 93-106.

Résultats de recherche: Contribution à un journal/une revueArticle

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