# Optimization demo¶

Date: | 2009-07-13 (last modified), 2006-02-10 (created) |
---|

SciPy's optimization package is scipy.optimize. The most basic non-linear optimization functions are:

```
* optimize.fmin(func, x0), which finds the minimum of func(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 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.

In [1]:

```
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()
```

*Section author: SciPyDotOrg, Unknown[134], Unknown[135], Unknown[136]*