SciPy's optimization package is scipy.optimize. The most basic non-linear optimization functions are:
 *optimize.fmin(func, x0), which finds the minimum of f(x) starting x with x0 (x can be a vector)
 *optimize.fsolve(func, x0), which finds a solution to func(x) = 0 starting with x = x0 (x can be a vector)
 *optimize.fminbound(func, x1, x2), which finds the minimum of a scalar function func(x) for the range [x1,x2] (x1,x2 must be a scalar and func(x) must return a scalar) 
See the [http://docs.scipy.org/doc/scipy/reference/optimize.html scipy.optimze documentation] for details.

This is a quick demonstration of generating data from several Bessel functions and finding some local maxima using fminbound.  This uses ipython with the -pylab switch.

{{{#!python
from scipy import optimize, special
from numpy import *
from pylab import *

x = arange(0,10,0.01)

for k in arange(0.5,5.5):
     y = special.jv(k,x)
     plot(x,y)
     f = lambda x: -special.jv(k,x)
     x_max = optimize.fminbound(f,0,6)
     plot([x_max], [special.jv(k,x_max)],'ro')

title('Different Bessel functions and their local maxima')
show()


}}}

{{{
#!figure
#class left
inline:NumPyOptimizationSmall.png

Optimization Example
}}}
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CategoryCookbook