I am familiarizing myself with CVXPY, and encountered a strange problem. I have the following simple toy optimization problem:
import numpy as np
import cvxpy as cp
A=np.array([[1,0,0],[0,1,0], [0,0,1]])
y=np.array([1,1,1])
# Upper bound for the constraint term
upper=1
# Solve the optimization problem using CVXPY
x = cp.Variable(3)
objective = cp.Minimize(cp.sum_squares(x))
constraint = [cp.sum_squares(A*x - y) <= upper]
prob = cp.Problem(objective, constraint)
prob.solve()
optimal_x = x.value
print('Value of constraint at optimal x:' + str(np.linalg.norm(A*optimal_x - y)**2))
Now, I expect my output number to be samller than upper=1
, but what I get is the following:
Value of constraint at optimal x:3.0000000068183947
I am very confused about how this could be true. Am I using the function cp.sum_squares
incorrectly? Am I just setting up the optimization in a wrong way? Any help is appreciated!!