title: Custom minimizer based on Levenberg-Marquardt in scipy.optimize.basinhopping
body: <p>I'm having troubles to minimize a complex non linear function in python. This function is actually the chiSquare of a fitting model used to fit experimental data. In order to get the global minimum, I'm using the basinhopping function in scipy. This function is a wrapper of the minimize() function that adds some perturbation to look for different local minima. Right now my problem is that it has troubles to find the local minima.</p>
  
  <p>There are a bunch of solvers that can be used in minimize(), and since I'm using bounds I chose between 'L-BFGS-B', 'SLSQP' and 'TNC'. None of them really find local minima. Is there a method based on the popular Levenberg-Marquardt algorithm that can be use to minimize? Maybe this does not make sense otherwise it would be already implemented, but I can't understand why. </p>
  
  <p>My original idea was actually to use the leastsqbound function(<a href="https://pypi.python.org/pypi/leastsqbound" rel="nofollow">https://pypi.python.org/pypi/leastsqbound</a>) that I know is very good at providing accurate covariance matrix despide the bounds, and include it in a larger algorithm that would look for global minima (like the basinhopping function). Do you know if something like this already exist?</p>
  
  <p>Thanks a lot for you advices!</p>