code: def _special_minimize(fun, grad, x, tol_NM, tol):
      # Find good starting point by Nelder-Mead
      res_NM = minimize(
          fun,
          x,
          method="Nelder-Mead",
          options={"xatol": tol_NM, "fatol": tol_NM},
      )
      # Now refine via root finding on the gradient of the function, which is
      # more precise than minimizing the function itself.
      res = root(
          grad,
          res_NM.x,
          method="lm",
          options={"ftol": tol, "xtol": tol, "gtol": tol},
      )
      return res.x
  
imports: import itertools
  import warnings
  from functools import partial
  import numpy
  import pytest
  import scipy
  from numpy.testing import assert_allclose
  from scipy import linalg
  from scipy.optimize import minimize, root
  from sklearn._loss import HalfBinomialLoss, HalfPoissonLoss, HalfTweedieLoss
  from sklearn._loss.link import IdentityLink, LogLink
  from sklearn.base import clone
  from sklearn.datasets import make_low_rank_matrix, make_regression
  from sklearn.exceptions import ConvergenceWarning
  from sklearn.linear_model import GammaRegressor, PoissonRegressor, Ridge, TweedieRegressor
  from sklearn.linear_model._glm import _GeneralizedLinearRegressor
  from sklearn.linear_model._glm._newton_solver import NewtonCholeskySolver
  from sklearn.linear_model._linear_loss import LinearModelLoss
  from sklearn.metrics import d2_tweedie_score, mean_poisson_deviance
  from sklearn.model_selection import train_test_split
label_desc: Use image node_id 1 for calling a global function with example usage: _special_minimize(fun, grad, x, tol_NM, tol) and returns: res