How to force larger steps on scipy.optimize functions?
I realize this is an old question but I haven't been able to find many discussion of similar topics. I am facing a similar issue with scipy.optimize.least_squares. I found that xtol did not do me much good. It did not seem to change the step size at all. What made a big difference was diff_step. This sets the step size taken when numerically estimating the Jacobian according to the formula step_size = x_i*diff_step, where x_i is each independent variable. You are using fmin so you aren't calculating Jacobians, but if you used another scipy function like minimize for the same problem, this might help you.
I have a function compare_images(k, a, b) that compares two 2d-arrays a and b
Inside the funcion, I apply a gaussian_filter with sigma=k to a My idea is to estimate how much I must to smooth image a in order for it to be similar to image b
The problem is my function compare_images will only return different values if k variation is over 0.5, and if I do fmin(compare_images, init_guess, (a, b) it usually get stuck to the init_guess value.
I believe the problem is fmin (and minimize) tends to start with very small steps, which in my case will reproduce the exact same return value for compare_images, and so the method thinks it already found a minimum. It will only try a couple times.
Is there a way to force fmin or any other minimizing function from scipy to take larger steps? Or is there any method better suited for my need?
EDIT:
I found a temporary solution.
First, as recommended, I used xtol=0.5 and higher as an argument to fmin.
Even then, I still had some problems, and a few times fmin would return init_guess.
I then created a simple loop so that if fmin == init_guess, I would generate another, random init_guess and try it again.
It's pretty slow, of course, but now I got it to run. It will take 20h or so to run it for all my data, but I won't need to do it again.
Anyway, to better explain the problem for those still interested in finding a better solution:

I have 2 images, A and B, containing some scientific data.
A looks like a few dots with variable value (it's a matrix of in which each valued point represents where a event occurred and it's intensity)
B looks like a smoothed heatmap (it is the observed density of occurrences)
B looks just like if you applied a gaussian filter to A with a bit of semi-random noise.
We are approximating B by applying a gaussian filter with constant sigma to A. This sigma was chosen visually, but only works for a certain class of images. 
I'm trying to obtain an optimal sigma for each image, so later I could find some relations of sigma and the class of event showed in each image.

Anyway, thanks for the help!