## Abstract

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.

Original language | English |
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Pages (from-to) | 611-626 |

Number of pages | 16 |

Journal | Mathematical Programming |

Volume | 161 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 1 Jan 2017 |

## Keywords

- Constrained nonlinear optimization
- Evaluation complexity
- Worst-case analysis