bhh at xs4all.nl
Fri Oct 21 09:39:24 CEST 2016
> On 21 Oct 2016, at 06:00, Mike meyer <1101011 at gmx.net> wrote:
> Let's take a different view of the problem.
> Given f=(f_1,...,f_m):R^n -> R^m we want to minimize ||f(x)||.
> What distinguishes this from a general minimization problem is that you know the structure of the
> objective function F(x)=||f(x)||² and have the individual constituents f_j.
> Make use of that information as appropriate.
> This is more general than trying to solve the system f(x)=0 or fitting a model to data.
> In this more general setting notions such as underdetermined/overdetermined system do not apply.
> The restricted view of model fitting serves only to confuse the issue.
> For that reason it is (in my view) a bad idea to force the user to set up his problem in
> R-model notation.
I assume that you have been referring to the R package minpack.lm.
I've had a look at the underlying Fortran code (from Minpack and developed by More et.al. made in a distant past) as used by the package.
That underlying code returns an error when the condition: number of functions (m) >= the number of independent variables (n)
is not satisfied i.e. when m < n.
Making that more general would entail a lot of thinking and reworking of the code. As far as I can see it is not possible to just remove the condition m>=n from the underlying Fortran. More (possibly many) changes would be required. Blaming R and/or the package author/maintainer is unfair.
If you require a more general version of the algorithm or if you want something else you will have to roll your own package/code.
If you don't feel that minpack.lm is appropriate for your application and you want changes you'll have to discuss matters with Moré (http://www.mcs.anl.gov/~more/) if I got the correct link.
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