input: from typing import List
  
  def optimize_objective_function(x0: List[float]) -> List[float]:
      """
      Optimize the given objective function using the 'nelder-mead' method from scipy.optimize.minimize.
      
      >>> optimize_objective_function([0.0, 0.0, 0.0])
      [0.99999994, 1.99999988, 2.99999981]
      """
      from scipy.optimize import minimize
  
      def obj_func(x):
          return (x[0] - 1)**2 + (x[1] - 2)**2 + (x[2] - 3)**2
  
      res = minimize(obj_func, x0, method='nelder-mead', options={'xtol': 1e-8, 'disp': True})
      return res.x
output:     from scipy.optimize import minimize
  
      def obj_func(x):
          return (x[0] - 1)**2 + (x[1] - 2)**2 + (x[2] - 3)**2
  
      res = minimize(obj_func, x0, method='nelder-mead', options={'xtol': 1e-8, 'disp': True})
      return res.x