Projects per year

### 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. © 2012 Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society.

Original language | English |
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Pages (from-to) | 93-106 |

Number of pages | 14 |

Journal | Mathematical Programming |

Volume | 144 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 2014 |

### Keywords

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

## Fingerprint Dive into the research topics of 'On the complexity of finding first-order critical points in constrained nonlinear optimization'. 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

## How much patience do you have? Issues in complexity for nonlinear optimization

Philippe Toint (Invited speaker)

Activity: Talk or presentation types › Oral presentation

## How much patience do you have? Issues in complexity for nonlinear optimization

Philippe Toint (Speaker)

Activity: Talk or presentation types › Oral presentation

## Polytechnic University of Hong Kong

Philippe Toint (Visiting researcher)

Activity: Visiting an external institution types › Research/Teaching in a external institution

## Prizes

## Cite this

*Mathematical Programming*,

*144*(1-2), 93-106. https://doi.org/10.1007/s10107-012-0617-9