How to find the minimum of a function using fmin from scipy

In this example we will see how to use the function fmin to minimize a function. The function fmin is contained in the optimize module of the scipy library. It uses the downhill simplex algorithm to find the minimum of an objective function starting from a guessing point given by the user. In the example we will start from two different guessing points to compare the results. Here's the code:

import numpy
import pylab
from scipy.optimize import fmin

# objective function
rsinc = lambda x: -1 * numpy.sin(x)/x

x0 = -5 # start from x = -5
xmin0 = fmin(rsinc,x0)

x1 = -4 # start from x = -4
xmin1 = fmin(rsinc,x1)

# plot the function
x = numpy.linspace(-15,15,100)
y = rsinc(x)
pylab.plot(x,y)
# plot of x0 and the minimum found startin from x0
pylab.plot(x0,rsinc(x0),'bd',xmin0,rsinc(xmin0),'bo')
# plot of x1 and the minimum found startin from x1
pylab.plot(x1,rsinc(x1),'rd',xmin1,rsinc(xmin1),'ro')
pylab.axis([-15,15,-1.3,0.3])
pylab.show()

The function fmin will print some detail about the iterative process performed:

Optimization terminated successfully.
         Current function value: -0.128375
         Iterations: 18
         Function evaluations: 36
Optimization terminated successfully.
         Current function value: -1.000000
         Iterations: 19
         Function evaluations: 38

And the graphical result should be as follows:

The blue dot is the minimum found starting from the blue diamond (x=-5) and the red dot is the minimum found starting from the red diamond (x=-4). In this case, when we start from x=-5 fmin get stuck in a local minum and when we start from x=-4 fmin reaches the global minimum.