Projects per year

### Abstract

Evaluation complexity for convexly constrained optimization is considered and it is shown first that the complexity bound of O(ε-
^{−3∕2} ) proved by Cartis et al. (IMA J Numer Anal 32:1662–1695, 2012) for computing an ε-approximate first-order critical point can be obtained under significantly weaker assumptions. Moreover, the result is generalized to the case where high-order derivatives are used, resulting in a bound of (Formula presented) evaluations whenever derivatives of order p are available. It is also shown that the bound of (Formula presented) evaluations (ε-
_{P} and ε-
_{D} being primal and dual accuracy thresholds) suggested by Cartis et al. (SIAM J. Numer. Anal. 53:836–851, 2015) for the general nonconvex case involving both equality and inequality constraints can be generalized to yield a bound of (Formula presented) evaluations under similarly weakened assumptions.

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

Title of host publication | Springer Optimization and Its Applications |

Subtitle of host publication | Algorithms, Complexity and Applications |

Editors | Iannis Demetriou, Panos Pardalos |

Publisher | Springer Heidelberg |

Chapter | 1 |

Pages | 5-26 |

Number of pages | 22 |

ISBN (Electronic) | 978-3-030-12766-4 |

DOIs | |

Publication status | Published - Jun 2019 |

### Publication series

Name | Springer Optimization and Its Applications |
---|---|

Volume | 145 |

ISSN (Print) | 1931-6828 |

ISSN (Electronic) | 1931-6836 |

### Keywords

- Complexity theory
- Nonlinear optimization
- scaled optimality conditions

## Fingerprint Dive into the research topics of 'Evaluation complexity bounds for smooth constrained nonlinear optimization using scaled KKT conditions and high-order models'. Together they form a unique fingerprint.

## Projects

- 2 Active

## Complexity in nonlinear optimization

TOINT, P., Gould, N. I. M. & Cartis, C.

1/11/08 → …

Project: Research

## Activities

## Oxford University

Philippe Toint (Visiting researcher)

Activity: Visiting an external institution types › Visiting an external academic institution

## 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

## Prizes

## Cite this

*Springer Optimization and Its Applications: Algorithms, Complexity and Applications*(pp. 5-26). (Springer Optimization and Its Applications; Vol. 145). Springer Heidelberg. https://doi.org/10.1007/978-3-030-12767-1_2