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On the complexity of the steepest-descent with exact linesearches

Coralia Cartis(Coralia.Cartis***at***ed.ac.uk)
Nick Gould(nick.gould***at***stfc.ac.uk)
Philippe Toint(philippe.toint***at***fundp.ac.be)

Abstract: The worst-case complexity of the steepest-descent algorithm with exact linesearches for unconstrained smooth optimization is analyzed, and it is shown that the number of iterations of this algorithm which may be necessary to find an iterate at which the norm of the objective function's gradient is less that a prescribed $\epsilon$ is, essentially, a multiple of $1/\epsilon^2$, as is the case for variants of the same algorithms using inexact linesearches.

Keywords: complexity, steepest descent, nonlinear optimization

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Category 2: Nonlinear Optimization (Nonlinear Systems and Least-Squares )


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Entry Submitted: 09/09/2012
Entry Accepted: 09/09/2012
Entry Last Modified: 09/09/2012

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