Re: [eigen] Non linear equations solver

[Koldo Ramirez <koldo.ramirez@xxxxxxxxx>]

Hello all

I include additional info about using Minpack.

It exists Minpack version 2. Between other advantages it uses BLAS and LAPACK. This is the presentation (http://ftp.mcs.anl.gov/pub/MINPACK-2/README or http://www-new.mcs.anl.gov/otc/minpack/summary.html)
        
        ...
        MINPACK-2 software for 
        the solution of systems of nonlinear equations, 
        nonlinear least squares problems, and minimization problems.
        
        The initial software development work concentrated on the
        software for the solution of medium-scale problems on vector
        and shared-memory architectures. A Levenberg-Marquardt method 
        for nonlinear least squares and a trust region Newton method 
        for minimization problems are currently available.
        The BLAS and LAPACK routines have been used wherever possible
        to enhance performance on a variety of architectures.
        Current work centers on software for large-scale problems.
        A variable-storage variable metric method
        and a trust region Newton method are currently available.
        Future work will focus on software for distributed memory architectures.
        ...
        
It includes a test collection, for example see http://www.osti.gov/bridge/servlets/purl/79972-zsWGEn/webviewable/79972.pdf

The problem is in the license (http://ftp.mcs.anl.gov/pub/MINPACK-2/vmlm/README)

        ...
        Use of this software for commercial purposes is expressly prohibited
        without contacting 
        
           Jorge J. More'
           Mathematics and Computer Science Division
           Argonne National Laboratory
           9700 S. Cass Ave.
           Argonne, Illinois 60439-4844
           e-mail: more@xxxxxxxxxxx
        ...

OCTAVE implements uses Minpack for non linear equations solving. See the comments in Octave forums:

- Feb 2008 discussion about using Minpack not only for non linear equations solving but for non linear least squares too (http://www.nabble.com/minpack-code-for-least-squares--td15476241.html)

- Jan 2009 fsolve improvement announcement (http://www.nabble.com/fsolve-improvements-td21663596.html)
        
        ...
        ..., the old minpack code is gone. ...
        Essentially the same method as in minpack is used - double dogleg
        trust region steps with Broyden updating of the jacobian. For large
        enough (no. of variables > 10) square and overdetermined(!) systems,
        the QR factorization of the jacobian is updated rather than the
        jacobian itself, avoiding costly re-factorizations. Broyden updating
        may be switched off by the user, yielding plain levenberg-marquardt
        method. 
        ...
        
Best regards
Koldo