[Python] BFGS algorithm finding almost good parameters but not converging with scipy.minimize()

I am estimating an Interval Regression model. I wrote my likelihood function (see intreg, STATA) as stated bellow, and compared my results with STATA. I am finding almost exactly (within 0.001) same parameters as STATA but the BFGS algorithm seems still not to converge.

I still get the following message :

message: Desired error not necessarily achieved due to precision loss.
success: False
status: 2
fun: 26435.40918822449
x: [ 7.379e+00 -6.967e-02 ... 2.149e-01 4.295e-01]
nit: 94
jac: [-4.883e-04 0.000e+00 ... -2.441e-04 4.883e-04]
hess_inv: [[ 3.566e-04 -7.314e-05 ... -1.261e-04 -1.775e-06]
[-7.314e-05 5.599e-05 ... 3.216e-05 5.660e-07]
...
[-1.261e-04 3.216e-05 ... 4.981e-04 1.297e-06]
[-1.775e-06 5.660e-07 ... 1.297e-06 8.380e-06]]
nfev: 4235
njev: 121



The log-likelihood function:

def log_likelihood(params, x, y_lower, y_upper):
beta = params[:-1]
sigma = np.abs(params[-1])

z_upper = (y_upper - np.dot(x, beta)) / sigma
z_lower = (y_lower - np.dot(x, beta)) / sigma

epsilon = 1e-10
ll_interval = np.sum(np.log(np.clip(norm.cdf(z_upper) - norm.cdf(z_lower), epsilon, None)))

log_likelihood = ll_interval

return -log_likelihood



and the command that I use to minimize it:

initial_params = np.concatenate([np.zeros(X.shape[1]), [1.0]])
result = minimize(log_likelihood, initial_params, args=(X, y_lower, y_upper), method='BFGS', options={'disp':True})



Does someone has an idea of why the algorithm seems to converge but still giving message that it is not?

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