[R] Creatiing an R package for solving nonlinear system of equations was: RE: finding roots of multivariate equation

[Rob Creecy]

This seems useful, but it is important to note that the approach may not 
work well
unless the system of nonlinear equations is very well behaved and a good 
starting
point is chosen. A good explanation of the problems with this exact 
approach, that
is adding up the sums of squares of the individual functions,  is described
in Numerical Recipes for C, second edition, p 382 (see 
http://www.nrbook.com/a/bookcpdf.php)
Briefly there will often be a great number of local minima even when 
there is only a single
root of the original equations.

Rob





Ravi Varadhan wrote:
> Hi,
>
> I have written a simple function to solve a system of nonlinear equations. I
> have called it nlsolve().  It actually minimizes the squared-norm of the set
> of functions by calling optim().  It uses the BFGS algorithm within optim().
> Apart from this restriction, the user can pass all the arguments available
> in optim().  All the control parameters can be passed as in the call to
> optim().  I have attached a text file containing the source for nlsolve()
> and also a number of test problems illustrating the use of nlsolve().  Any
> feedback and suggestions to improve it are welcome.
>
> Hope this is useful.
>
> Best,
> Ravi.
>
> ----------------------------------------------------------------------------
> -------
>
> Ravi Varadhan, Ph.D.
>
> Assistant Professor, The Center on Aging and Health
>
> Division of Geriatric Medicine and Gerontology 
>
> Johns Hopkins University
>
> Ph: (410) 502-2619
>
> Fax: (410) 614-9625
>
> Email: rvaradhan at jhmi.edu
>
> Webpage:  http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
>
>
>
> ----------------------------------------------------------------------------
> --------
>
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Ravi Varadhan
> Sent: Wednesday, June 20, 2007 5:23 PM
> To: r-help at stat.math.ethz.ch
> Subject: [R] Creatiing an R package for solving nonlinear system of
> equations was: RE: finding roots of multivariate equation
>
> Hi All,
>
> Replying to this and numerous other requests in the past has made me realize
> that a nonlinear solver is very much needed for R users.  I have
> successfully used a nonlinear solver based on the spectral gradient method,
> in FORTRAN.  I can readily translate that to R and make it available as an R
> function, but what I would really like to do is to make that into a package.
> I can provide the R function and several test examples.  But I am not good
> at creating a good/reliable package.  So, it would be ideal if one of the R
> gurus is interested in collaborating with me on this project.  Any one
> interested?
>
> Ravi.
> ----------------------------------------------------------------------------
> -------
>
> Ravi Varadhan, Ph.D.
>
> Assistant Professor, The Center on Aging and Health
>
> Division of Geriatric Medicine and Gerontology 
>
> Johns Hopkins University
>
> Ph: (410) 502-2619
>
> Fax: (410) 614-9625
>
> Email: rvaradhan at jhmi.edu
>
> Webpage:  http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
>
>
>
> ----------------------------------------------------------------------------
> --------
>
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Bill Shipley
> Sent: Wednesday, June 20, 2007 1:37 PM
> To: r-help at stat.math.ethz.ch
> Subject: [R] finding roots of multivariate equation
>
> Hello,
> I want to find the roots of an equation in two variables.  I am aware of the
> uniroot function, which can do this for a function with a single variable
> (as I
> understand it...) but cannot find a function that does this for an equation
> with more than one variable.  I am looking for something implementing
> similar
> to a Newton-Raphson algorithm.
> Thanks.
>
>   
> ------------------------------------------------------------------------
>
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