Optimization – minimization

Before discussing how to generate an optimal portfolio, it is necessary to study a few optimization functions. In the following example, we minimize our objective function of y:

First, let's look at the graph of this objective function, see the following code:

import scipy as sp
import matplotlib.pyplot as plt
x=sp.arange(-5,5,0.01)
a=3.2
b=5.0
y=a+b*x**2
plt.plot(x,y)
plt.title("y= "+str(a)+"+"+str(b)+"x^2")
plt.ylabel("y")
plt.xlabel("x")
plt.show()

The graph is shown here:

To make the program more general, two coefficients of a and b are generated. Apparently, since the power of x is 2, y is minimized only when x is 0. The Python code for minimization is as follows:

from scipy.optimize import minimize
def myFunction(x):
    return (3.2+5*x**2)
x0=100
res = minimize(myFunction,x0,method='nelder-mead',options={'xtol':1e-8,'disp': True})

In the preceding program, the major function used is called the scipy.optimize.minimize() function. The first input is our objective...