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Abstract
An example is presented where Newton's method for unconstrained minimization is applied to find an $\epsilon$approximate firstorder 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 steepestdescent method in its worstcase. The novel feature of the proposed example is that the objective function has a globally Lipschitzcontinuous 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 

Publisher  Namur center for complex systems 
Number of pages  9 
Volume  032013 
Publication status  Published  5 May 2013 
Keywords
 Complexity theory, nonlinear optimization, Newton method
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 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 2016Activity: Talk or presentation types › Oral presentation

How much patience do you have? Issues in complexity for nonlinear optimization
Philippe Toint (Speaker)
31 Jan 2016Activity: Talk or presentation types › Oral presentation

Polytechnic University of Hong Kong
Philippe Toint (Visiting researcher)
31 Jan 2016 → 14 Feb 2016Activity: Visiting an external institution types › Research/Teaching in a external institution