Understanding optimization

In finance, many issues depend on optimization, such as choosing an optimal portfolio with an objective function and with a set of constraints. For those cases, we could use a SciPy optimization module called scipy.optimize. Assume that we want to estimate the x value that minimizes the value of y, where y =3 + x². Obviously, the minimum value of y is achieved when x takes a value of 0.

>>>import scipy.optimize as optimize 
>>>def my_f(x):
       Return 3 + x**2
>>>optimize.fmin(my_f,5)   # 5 is initial value
     Optimization terminated successfully
     Current function values: 3:000000
     Iterations: 20
     Function evaluations: 40
Array([ 0. ])

To find a list of all input variables to this fmin() function and their meanings, issue help(optimize.fmin). To list all the functions included in scipy.optimize, issue dir(optimize).