Projects per year

### Abstract

An example is presented where Newton's method for unconstrained minimization is applied to find an $\epsilon$-approximate first-order critical point of a smooth function and takes a multiple of $\epsilon^{-2}$ iterations and function evaluations to terminate, which is as many as the steepest-descent method in its worst-case. The novel feature of the proposed example is that the objective function has a globally Lipschitz-continuous Hessian, while a previous example published by the same authors only ensured this critical property along the path of iterates, which is impossible to verify \emph{a priori}.

Original language | English |
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Publisher | Namur center for complex systems |

Number of pages | 9 |

Volume | 03-2013 |

Publication status | Published - 5 May 2013 |

### Keywords

- Complexity theory, nonlinear optimization, Newton method

## Fingerprint Dive into the research topics of 'An example of slow convergence for Newton's method on a function with globally Lipschitz continuous Hessian'. Together they form a unique fingerprint.

## Projects

- 1 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)

5 Feb 2016

Activity: Talk or presentation types › Oral presentation

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

Philippe Toint (Speaker)

31 Jan 2016

Activity: Talk or presentation types › Oral presentation

## Polytechnic University of Hong Kong

Philippe Toint (Visiting researcher)

31 Jan 2016 → 14 Feb 2016

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

## Cite this

Cartis, C., Gould, N. I. M., & Toint, P. (2013).

*An example of slow convergence for Newton's method on a function with globally Lipschitz continuous Hessian*. Namur center for complex systems.