In cyclic coordinate search, we look for an optimum inline with each one of the coordinate axes. I have defined the variable x_new as an updated variable for the start point. Inside the loop, the objective function is minimized first in the x1 direction and then the x2 direction.
I am having trouble actually updating x_new. It will not update as currently coded and when printed is output as [0, 0].
import scipy.optimize as opt
import numpy as np
# Objective Function
# f(x1,x2) = (x2-x1**2)**4 + (3-x1)**2
# x = [0, 0]
# Initialize
x0 = np.array([0, 0])
iter = 0
epsilon = 0.0001
x_new = x0
for i in range(len(x0)):
if i == 0:
def obj_func(x):
return (x_new[1] - x ** 2) ** 4 + (3 - x) ** 2
x_new[0] = opt.minimize_scalar(obj_func).x
else:
def obj_func(x):
return (x - x_new[0]**2) ** 4 + (3 - x_new[0]) ** 2
x_new[1] = opt.minimize_scalar(obj_func).x
iter += 1
print(x_new)
print(iter)
This is the output of this code
How can I get x_new to update or am I approaching this all wrong?
The issue was that I didn't define the numpy arrays as floats so it wouldn't update the original assignment of x_new
import scipy.optimize as opt
import numpy as np
# Objective Function
# f(x1,x2) = (x2-x1**2)**4 + (3-x1)**2
# x = [0, 0]
x_new = np.array([0.0, 0.0])
x0 = np.array([0.0, 0.0])
x_hist = np.array([0.0, 0.0])
f = np.array([9])
iter = 0
while iter < 12:
for i in range(len(x0)):
if i == 0:
def obj_func(x):
return (x_new[1] - x ** 2) ** 4 + (3 - x) ** 2
x_new[0] = opt.minimize_scalar(obj_func).x
f = np.append(f, obj_func(x_new[0]))
x_hist = np.append(x_hist, x_new[0])
iter += 1
else:
def obj_func(x):
return (x - x_new[0] ** 2) ** 4 + (3 - x_new[0]) ** 2
x_new[1] = opt.minimize_scalar(obj_func).x
x_hist = np.append(x_hist, x_new[1])
f = np.append(f, obj_func(x_new[1]))
iter += 1
print('The optimum value found after', iter, 'iterations is f* = ',
round((x_new[1] - x_new[0] ** 2) ** 4 + (3 - x_new[0]) ** 2, 5),
'\nThe optimizers were x* = ', x_new, '\nThe minimum was found using',
'Cyclic Coordinate Search w/o acceleration')