On the Relationship between the Convergence Rates of Iterative and Continuous Processes

On the Relationship between the Convergence Rates of Iterative and Continuous Processes

Considering iterative sequences that arise when approximate solutions $x_k$ to a numerical problem are updated by $x_{k+1} = x_k+v(x_k)$, where $v$ is a differentiable vector field, we derive necessary and sufficient conditions for such discrete processes to converge to a stationary point of $v$ at...

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Veröffentlicht in:SIAM journal on optimization 2007-01, Vol.18 (1), p.52-64
Hauptverfasser: Hauser, Raphael, Nedić, Jelena
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Approximation
Dynamical systems
Optimization
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Nedić, Jelena
description Considering iterative sequences that arise when approximate solutions $x_k$ to a numerical problem are updated by $x_{k+1} = x_k+v(x_k)$, where $v$ is a differentiable vector field, we derive necessary and sufficient conditions for such discrete processes to converge to a stationary point of $v$ at different Q-rates in terms of a similar notion of fast convergence for the corresponding continuous processes.
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subjects Approximation
Dynamical systems
Optimization
title On the Relationship between the Convergence Rates of Iterative and Continuous Processes
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