Hauser, Raphael and Nedic, Jelena (2003) The continuous NewtonRaphson method can look ahead. Technical Report. Unspecified. (Submitted)

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Abstract
This paper is about an intriguing property of the continuous NewtonRaphson 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 NewtonRaphson 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, then the two flux lines through x defined by the NewtonRaphson vector fields that correspond to f and F differ from one another only within D.
The work was supported by EPSRC grant GR/S34472 (R. Hauser) and by the Clarendon Fund, Oxford University Press and ORS Award, Universities UK (J Nedic)
Item Type:  Technical Report (Technical Report) 

Subjects:  D  G > Global analysis, analysis on manifolds H  N > Numerical analysis 
Research Groups:  Numerical Analysis Group 
ID Code:  1202 
Deposited By:  Lotti Ekert 
Deposited On:  18 May 2011 07:11 
Last Modified:  29 May 2015 18:53 
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