[SciPy-User] ODR , Levenberg-Marquardt, non linear fitting and convergence: some assistance needed

[ms]

Hi,

I am currently smashing my head on the following problem.

I am trying to fit data to two equations, which are two levels of 
approximation for the same model. I am currently using ODR to fit.

Of course the 2nd order approximation is mathematically bit more 
complicated than the first, involving a long summatory etc. but the 
resulting curve and behaviour are overall very similar.

Now, in my tests, the 1st order approx. usually converges, while the 2nd 
order does not converge at all: not that it gives some wrong result, it 
remains stuck to the initial parameters with zero values in the 
covariance, etc. This even when I feed to ODR starting values very close 
to the "true" ones.

I used fmin so far to bypass this problem, but it is really slow. 
Recently a collegue of mine told me that he can get Levenberg-Marquardt 
to minimize the untreatable (in my system) 2nd order approx, using 
Mathematica, out of the box.

I have no idea unfortunately what are the differences between the 
Mathematica and the ODRPACK implementations of Levenberg-Marquardt, but 
if one can do it I think the other one can too. So, what should I try to 
improve my system? I tried increasing iterations, fixing X values etc. 
but nothing seems to work properly. Do you have any hint?

Thanks a lot!
M.