Scipy optimizer doesn't properly converge

scipy_vs_cvxpy.py

"""constrained LLSQ"""

"""scipy.minimize"""

import numpy as np
from scipy import optimize
from scipy import linalg

# Generate random problem data.
m = 30
n = 20
np.random.seed(1)
X = np.random.randn(m, n)
y = np.random.randn(m)


def obj(theta, X, y):
    return linalg.norm(a=(np.dot(X, theta0) - y), ord=2)
    

args = (X, y)
bounds = [(0.0, 1.0)] * n
theta0 = np.full((n), 0.9) # try 0.1, 0.2, 0.5, 0.7, etc.

method = 'SLSQP'
tol = 1e-8

opt = optimize.minimize(obj, theta0, method=method, args=args, bounds=bounds, tol=tol)
opt

"""
fun: 21.6995803953911
     jac: array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
       0., 0., 0.])
 message: 'Optimization terminated successfully'
    nfev: 21
     nit: 1
    njev: 1
  status: 0
 success: True
       x: array([0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9,
       0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9])
"""

"""cvxpy"""
import cvxpy as cp
import numpy as np

# Generate random problem data.
m = 30
n = 20
np.random.seed(1)
X = np.random.randn(m, n)
y = np.random.randn(m)

# Construct the problem.
theta = cp.Variable(n)
objective = cp.Minimize(cp.sum_squares(X*theta - y))
constraints = [0 <= theta, theta <= 1]
prob = cp.Problem(objective, constraints)

# The optimal objective value is returned by `prob.solve()`.
result = prob.solve()
# The optimal value for theta is stored in `theta.value`.
print(result)
print(theta.value)

"""
19.83126370644502
[-1.79109255e-19  2.85112420e-02  2.79973443e-19  3.37658729e-20
 -2.72802663e-19  1.49285011e-01 -9.94082533e-20  8.35373900e-20
  2.46718649e-01  5.78224144e-01 -4.03739463e-19  1.01242860e-03
 -9.28486180e-20  2.26767464e-01 -1.58813678e-19 -8.97232272e-20
 -1.22145729e-19 -1.51509428e-19  1.12060672e-19 -3.48318635e-19]
"""