🚀 go-pugleaf

I'm looking for an algorithm that can solve underdetermined nonlinear least
square problems:

           T
     Min (R .R)     where R    is a nonlinear vector function of X
                           mx1                                    nx1

     and m<n.


The Gauss-Newton algorithm converges quadratically for zero residual
problems (ZRP) but converges very slowly for large residual problems.
The LRP can be solved faster using BFGS for instance.
Now, I need a routine that can solve both ZRP and LRP with at least
superlinear convergence.
Fletcher and Xu, have proposed a hybrid algorithm (combination of GN and
BFGS) for overdetermined problems (m>n), but this cannot by easily adapted
for underdetermined problems (the Hessian appoximation J'*J will always be
singular)

Any hints ??

  ** Chris **

Chris J.J. Paredis				Email: Paredis@cmu.edu
Electrical and Computer Engineering		phone: (412)-268-7121
The Robotics Institute				Carnegie - Mellon University