# Why is Levenberg-Marquardt only used with least squares problem?

I've noticed the Levenberg-Marquardt algorithm is only used with least squares problem and I didn't find any library in R or Python which allow to minimise the absolute values of the residual (and not the square of the residual)

1. Is there any reason of that ?
2. Does it make sense to apply sqrt(abs(residual)) on the residual before it's been squared if we want to use this algorithm with Least Absolute Deviation instead of Least Squares Deviation ?
• Is it because sqrt(abs(x)) is not differentiable when x=0 ? – psql Oct 28 '15 at 11:48