[R] How is the Gauss-Newton method compared to Levenberg-Marquardt for curve-fitting?

[Ali -]

Hi,

It seems to me that the most suitable method in R for curve-fitting is the use of nls, which uses a Gauss-Newton (GN) algorithm, while the use of the Levenberg-Marquardt (LM) algorithm does not seem to be very stressed in R. According to this [1] by Ripley, 'Levenberg-Marquardt is hardly competitive these days' which could imply the low emphasize on LM in R.

The position of LM is, to some extend, confusing. Bonnans et al [2] introduce the trust-region-based method of LM like this:

'This chapter is mostly devoted to methods which, although less "universal"
than the preceding, are useful in a good number of cases. The frst one (trust-region)
is actually extremely important, and might supersede line-searches,
sooner or later.'

The above should demonstrate the contradiction.

Since some R developers are indeed the pioneers in the optimisation theory, I would like to ask for references involving profiling of various methods, including more modern techniques, with an application in general model-fitting.




[1] http://tolstoy.newcastle.edu.au/R/help/00b/2492.html

[2] Numerical Optimization, 2nd ed
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