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### The continuous Newton-Raphson method can look ahead

Abstract:

This paper is about an intriguing property of the continuous Newton-Raphson method for the minimization of a continuous objective function f: if x is a point in the domain of attraction of a strict local minimizer x* then the flux line of the Newton-Raphson flow that starts in x approaches x* from a direction that depends only on the behavior of f in arbitrarily small neighborhoods around x and x*. In fact, if F is a sufficiently benign perturbation of f on an open region D not containing x, ...

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### Authors

Raphael Hauser More by this author
Jelena Nedic More by this author
Publication date:
2003-08-05
URN:
uuid:306ae4fd-8615-4756-8769-70561f2271a4
Local pid:
oai:eprints.maths.ox.ac.uk:1202