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### Abstract

The worst-case evaluation complexity for smooth (possibly nonconvex) unconstrained optimization is considered. It is shown that, if one is willing to use derivatives of the objective function up to order p (for p≥ 1 ) and to assume Lipschitz continuity of the p-th derivative, then an ϵ-approximate first-order critical point can be computed in at most O(ϵ
^{-}
^{(}
^{p}
^{+}
^{1}
^{)}
^{/}
^{p}) evaluations of the problem’s objective function and its derivatives. This generalizes and subsumes results known for p= 1 and p= 2.

Original language | English |
---|---|

Pages (from-to) | 359-368 |

Number of pages | 10 |

Journal | Mathematical Programming |

Volume | 163 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 15 Apr 2017 |

### Keywords

- Evaluation complexity
- High-order models
- Nonlinear optimization
- Regularization
- Unconstrained optimization

## Fingerprint Dive into the research topics of 'Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models'. Together they form a unique fingerprint.

## Activities

- 6 Invited talk

## Worst-case evaluation complexity for nonconvex optimization: adventures in the jungle of high-order nonlinear optimization

Philippe Toint (Speaker)

Activity: Talk or presentation types › Invited talk

## A path and some adventures in the jungle of high-order nonlinear optimization

Philippe Toint (Speaker)

Activity: Talk or presentation types › Invited talk

## A path and some adventures in the jungle of high-order nonlinear optimization

Philippe Toint (Speaker)

Activity: Talk or presentation types › Invited talk

## Cite this

*Mathematical Programming*,

*163*(1-2), 359-368. https://doi.org/10.1007/s10107-016-1065-8