I'm learning about the application of numerical optimization, and noticed that in one of the programs that I'm using it uses Powell's method to get parameters of a piece-wise function, and Levmar if the function can be expressed as a simple formula (such as $x^a + b$). I think non-linear least squares (Levmar) could have been used for both.
I wanted to understand when to use Powell's method and when to use Levmar?
A specific question I have is given reasonable initial starting points to both, will both of them converge to the same minimum?
