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Raphael Hauser (hausercomlab.ox.ac.uk) 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. Keywords: Continuous Newton method, NewtonRaphson method, Newton flow, qualitative analysis Category 1: Nonlinear Optimization (Unconstrained Optimization ) Citation: Research report NA03/05, Oxford University Computing Laboratory, August 2003 Download: [Postscript] Entry Submitted: 08/05/2003 Modify/Update this entry  
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