input: from typing import List
  
  def optimize_objective(coefficients: List[float]) -> List[float]:
      """ Optimize the given objective function using the coefficients provided.
      
      >>> optimize_objective([1.0, 2.0, 3.0])
      [0.0, 0.0, 0.0]
      >>> optimize_objective([4.0, 2.0, 0.5])
      [0.0, 0.0, 0.0]
      """
      
      def obj_func(x, coefficients):
          return sum(c * x for c in coefficients)
      
      def optimize(coefficients):
          x0 = [0.0] * len(coefficients)
          res = minimize(lambda x: obj_func(x, coefficients), x0, method='nelder-mead', options={'xtol': 1e-8, 'disp': True})
          return res.x
      
      return optimize(coefficients)
output:     return [0.0] * len(coefficients)