Optimization Online


The continuous Newton-Raphson method can look ahead

Raphael Hauser (hauser***at***comlab.ox.ac.uk)
Jelena Nedic (jelena***at***comlab.ox.ac.uk)

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, then the two flux lines through x defined by the Newton-Raphson vector fields that correspond to f and F differ from one another only within D.

Keywords: Continuous Newton method, Newton-Raphson method, Newton flow, qualitative analysis

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Citation: Research report NA-03/05, Oxford University Computing Laboratory, August 2003

Download: [Postscript]

Entry Submitted: 08/05/2003
Entry Accepted: 08/05/2003
Entry Last Modified: 08/05/2003

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Programming Society