### 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 originale | Anglais |
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Pages (de - à) | 611-626 |

Nombre de pages | 16 |

journal | Mathematical Programming |

Volume | 161 |

Numéro de publication | 1-2 |

Les DOIs | |

état | Publié - 1 janv. 2017 |

### Empreinte digitale

### Citer ceci

*Mathematical Programming*,

*161*(1-2), 611-626. https://doi.org/10.1007/s10107-016-1016-4

}

*Mathematical Programming*, VOL. 161, Numéro 1-2, p. 611-626. https://doi.org/10.1007/s10107-016-1016-4

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

Résultats de recherche: Contribution à un journal/une revue › Article

TY - JOUR

T1 - On the complexity of finding first-order critical points in constrained nonlinear optimization

T2 - Corrigendum

AU - Cartis, C.

AU - Gould, N. I.M.

AU - Toint, Ph L.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

KW - Constrained nonlinear optimization

KW - Evaluation complexity

KW - Worst-case analysis

UR - http://www.scopus.com/inward/record.url?scp=84965081659&partnerID=8YFLogxK

U2 - 10.1007/s10107-016-1016-4

DO - 10.1007/s10107-016-1016-4

M3 - Article

AN - SCOPUS:84965081659

VL - 161

SP - 611

EP - 626

JO - Mathematical Programming

JF - Mathematical Programming

SN - 0025-5610

IS - 1-2

ER -