Python opt.minimize

Python opt.minimize is routine at Python programming language that searches the minimum of a given function.

Example of the code with single variabe

import scipy.optimize as opt
def func(x):
 return (x-123)**2
x0 = 0
res = opt.minimize(func, x0)
print(res)

Output generated:

   status: 0
  success: True
     njev: 4
     nfev: 12
 hess_inv: array([[ 0.5]])
      fun: 5.553105828993429e-17
        x: array([ 122.99999999])
  message: 'Optimization terminated successfully.'
      jac: array([ -2.67164069e-12])

The sixth element of the returned array seems to contain the array, and the zeroth element of the array is extremum (123) that realizes the minimal value (zero) of the function func.

Example of the code with 2 variables

import scipy.optimize as opt
def func(x):
 return ( x[0]-123)**2 + (x[1]-3.14159)**2
x0 = [0,0]
res = opt.minimize(func, x0)
print(res.x)

Expected output:

[ 123.00000006    3.14159   ]

Example of the code with function of 3 variables

import scipy.optimize as opt
def func(x):
 return  x[0]**4 + x[1]**4  + 8*x[0]*x[1] + x[2]**2 

x0 = [0.,0.,0.]
res = opt.minimize(func, x0)
print(res.x, res.fun)

x1 = [1.,-1.,1.]
res1 = opt.minimize(func, x1)
print(res1.x, res1.fun)

x2 = [-1.,1.,2.]
res2 = opt.minimize(func, x2)
print(res2.x, res2.fun)

Output:

(array([ 0.,  0.,  0.]), 0.0)
(array([  1.41421355e+00,  -1.41421356e+00,  -1.38110636e-08]), -7.999999999999997)
(array([ -1.41421367e+00,   1.41421367e+00,   3.97624677e-07]), -7.999999999999657)

References

https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html minimize(fun, x0, args=(), method=None, jac=None, hess=None, hessp=None, bounds=None, constraints=(), tol=None, callback=None, options=None)[source] Minimization of scalar function of one or more variables. Parameters: funcallable The objective function to be minimized. fun(x, *args) -> float where x is a 1-D array with shape (n,) and args is a tuple of the fixed parameters needed to completely specify the function. ..

Keywords

«Python»