# An example of slow convergence for Newton's method on a function with globally Lipschitz continuous Hessian

Coralia Cartis, N. I. M. Gould, Ph Toint

Research output: Working paper

### 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 Namur center for complex systems 9 03-2013 Published - 5 May 2013

### Keywords

• Complexity theory, nonlinear optimization, Newton method

## Complexity in nonlinear optimization

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

1/11/08 → …

Project: Research

## Activities

• 4 Oral presentation
• 3 Research/Teaching in a external institution
• 1 Visiting an external academic institution

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

Philippe Toint (Invited speaker)

5 Feb 2016

Activity: Talk or presentation typesOral presentation

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

Philippe Toint (Speaker)

31 Jan 2016

Activity: Talk or presentation typesOral presentation

## Polytechnic University of Hong Kong

Philippe Toint (Visiting researcher)

31 Jan 201614 Feb 2016

Activity: Visiting an external institution typesResearch/Teaching in a external institution