[R] Matlab's lsqnonlin

[Katharine Mullen]

>
> I'm wondering about experiences:
> Do you know of cases where  minpack.lm's  nls.lm() solved a
> (real) problem that nls() would have a problem with ?
>

In short, no.  However, I looked at this question in the limited context
of fitting the parameters of a linear superposition of 2 exponentials with
Gaussian noise.  A simulation study showed nearly identical performance
for the range of parameter values/noise levels that are of practical
interest to us.

Are there problems for which steepest descent gets you in the neighborhood
of a solution whereas GN does not?  If such problems exist then there
would be reason to apply LM instead of GN, but I don't know of any.

> Beware however -- one of the main things I learned about this
> field from Doug Bates, co-author of Bates_and_Watts and
> prinicipal author of S's and R's nls() :
> It's a *feature* that nls() does not converge sometimes when
> other methods do falsely claim convergence!
>
> Martin Maechler, ETH Zurich
>
>     KateM> ----
>     KateM> Katharine Mullen
>     KateM> mail: Department of Physics and Astronomy, Faculty of Sciences
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>
>
>     KateM> On Fri, 7 Sep 2007, Jose Luis Aznarte M. wrote:
>
>     >> Hi! I'm translating some code from Matlab to R and I found a problem.
>     >> I need to translate Matlab's function 'lsqnonlin'
>     >> (http://www-ccs.ucsd.edu/matlab/toolbox/optim/lsqnonlin.html) into R,
>     >> and at the beginning I  thought it would be the same as R's 'optim'. But
>     >> then I looked at the definition of 'lsqnonlin' and I don't quite see how
>     >> to make 'optim' to do the same thing. Does anyone have an idea?
>     >> This is apart from the fact that I would like to use the Levenberg
>     >> Marquardt algorithm which is not implemented in R (some discussion about
>     >> this: http://tolstoy.newcastle.edu.au/R/help/00b/2492.html).
>     >> Thank you! All the best,
>     >>
>     >>
>     >> --                                                      --
>     >> Jose Luis Aznarte M.       http://decsai.ugr.es/~jlaznarte
>     >> Department of Computer Science and Artificial Intelligence
>     >> Universidad de Granada           Tel. +34 - 958 - 24 04 67
>     >> GRANADA (Spain)                  Fax: +34 - 958 - 24 00 79
>     >>
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>
>     KateM> ______________________________________________
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>     KateM> and provide commented, minimal, self-contained, reproducible code.
>