From: jarausch@igpm.rwth-aachen.de (Helmut Jarausch)
Newsgroups: sci.math.num-analysis
Subject: Re: Q: constrained non-lin-fit
Date: 6 Oct 1995 13:54:41 GMT

In article <4510d8$3f2@rrzs3.uni-regensburg.de>, c4294@rrzc4 (Wolfgang
Schildbach) writes:
> Hello,
> 
> I am using the Levenberg-Marquardt method for non-linear fits as given in
> Numerical Recipes in C, pages 685 ff. (function mrqmin())
> 
> the function to fit for is log(b/(1+c*x^2)) with b and c being the parameters
> to fit.
> 
> Sometimes I find that the fitting routine will have tried a value of c<0 or
> b<0
> which gives me trouble with the logarithm.
> 
> Is there an easy way to constrain parameters a,b, in particular with the
> func-
> tion mrqmin()?
> 

You can use the package L-BFGS-B which seems to be a very good code.
Here the README from it:

From: Jorge Nocedal <nocedal@venus.eecs.nwu.edu>
Date: Thu, 1 Jun 1995 11:39:25 -0500
Subject: New Optimization Code

We would like to announce the availability of a new
code for solving large nonlinear optimization problems
with bounds on the variables.

The program, called L-BFGS-B, implements a limited memory BFGS
algorithm. The user must supply the gradient g of f, but knowledge 
about the Hessian matrix is not required. This program is an
extension of algorithm L-BFGS (Harwell routine VA15) which can handle 
only unconstrained problems.

Both codes can be obtained via anonymous ftp at eecs.nwu.edu.
They are in the directories pub/lbfgs and pub/lbfgs.unc.
More detailed information can be obtained at
http://www.eecs.nwu.edu/~ciyou or http://www.eecs.nwu.edu/~nocedal

Ciyou Zhu, Richard Byrd and Jorge Nocedal

==============================================================================

Newsgroups: sci.math.num-analysis,comp.lang.fortran
From: Giorgio Pauletto <pauletto@uni2a.unige.ch>
Subject: Re: [Q] Is there any software that has implemented the Broyden's algorithm?
Date: Thu, 5 Oct 1995 07:08:20 GMT

mori@wilshire.math.ucla.edu (Mortaza Jamshidian) wrote:
>
>Is there any software package that has implemented the Boryden's 
>algorithm for solving systems of nonlinear equations? The algorithm
>that I am refering to is a quasi newton algorithm by Broyden (1969).
>
>Thanks ahead of time for any info.
>Mori
>

I think Dennis and Schnabel's book "Numerical Methods for Unconstrained
Optimization and Nonlinear Equations", Prentice Hall, 1983 contains
a good discussion about Broyden's update for nonlinear equations and
gives in its appendix detailed algorithms for its implementation.
Hope this may help.

-- Giorgio
+------------------------------------------------+
|  Giorgio Pauletto     pauletto@uni2a.unige.ch  |
|  http://www.unige.ch/ses/metri/pauletto        |
|  Dept of Econometrics                          |
|  University of Geneva, Switzerland             |
+------------------------------------------------+