Optimization Online


On the Relationship Between Convergence Rates of Discrete and Continuous Dynamical Systems

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

Abstract: Considering iterative sequences that arise when the approximate solution $x_k$ to a numerical problem is updated by $x_{k+1} = x_k+v(x_k)$, where $v$ is a vector field, we derive necessary and sufficient conditions for such discrete methods to converge to a stationary point of $v$ at different Q-rates in terms of the differential properties of $v$ and in terms of the asymptotic dynamical behaviour of the associated continuous dynamical system.

Keywords: Q-convergence, superlinear convergence

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Citation: Research report NA-04/10, Oxford University Computing Laboratory, May 2004

Download: [Postscript]

Entry Submitted: 06/02/2004
Entry Accepted: 06/02/2004
Entry Last Modified: 06/02/2004

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