I have an optimization problem that I'm solving using matlab, I didn't pay much attention to what kind of problem was except that it wasn't linear. So I solved it using a quasi-newton algorithm. However I realized this morning that my problem can be written in the form
$$ f(x) = \frac{1}{2}\sum_j r_j(x)^2 $$
Which should allow me to use an LM (Levemberg-Marquadt) solver. I do wonder however in case I'd switch what kind of benefit LM can give me over the current algorithm.
Can it be faster much faster maybe?
As far as I know quasi-newton are a family of direction search algorithm, while LM is a special case of trust region approach specialized for non linear least square (according to my references at least).
I can see a possible memory advantage, because in my case the Jacobian would be sparse, but what about speed? is there anything I can say?