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A maximum curvature step and geodesic displacement for nonlinear least squares descent algorithms

Abstract : We adress in this paper the choice of both the step and the curve of the parameter space to be used in the line search search part of descent algorithms for the minimization of least squares objective functions. Our analysis is based on the curvature of the path of the data space followed during the line search. We define first a new and easy to compute maximum curvature step, which gives a guaranteed value to the residual at the next iterate, and satisfies a linear decrease condition with =. Then we optimize (i.e. minimize !) the guaranteed residual by performing the line search along a curve such that the corresponding path in the data space is a geodesic of the output set. An inexpensive implementation using a second order approximation to the geodesic is proposed. Preliminary numerical comparisons of the proposed algorithm with two versions of the Gauss-Newton algorithm show that it works properly over a wide range of nonlinearity, and tends to outperform its competitors in strongly nonlinear situations.
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Submitted on : Tuesday, May 23, 2006 - 8:04:39 PM
Last modification on : Friday, February 4, 2022 - 3:07:22 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:58:25 PM


  • HAL Id : inria-00072205, version 1



Guy Chavent. A maximum curvature step and geodesic displacement for nonlinear least squares descent algorithms. [Research Report] RR-4383, INRIA. 2002. ⟨inria-00072205⟩



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