input: from typing import List
  
  def optimize_objective_function(objective_function: str, initial_guess: List[float]) -> List[float]:
      """ Optimize the given objective function using the Nelder-Mead method starting from 
      the provided initial guess. The function should return the optimized values of the 
      variables.
      >>> optimize_objective_function("2*x[0]**2 + x[1]**2 + 2*x[0] + x[1]", [0.0, 0.0])
      [-0.49999999084065825, -0.499999990784237]
      """
output:     from scipy.optimize import minimize
      import numpy as np
  
      def objective(x):
          return eval(objective_function)
  
      result = minimize(objective, initial_guess, method='Nelder-Mead')
      return result.x