code: def apply_optimizer(
      optimizer,
      x0,
      f=None,
      df=None,
      f_df=None,
      duplicate_manager=None,
      context_manager=None,
      space=None,
  ):
      """
      :param x0: initial point for a local optimizer (x0 can be defined with or without the context included).
      :param f: function to optimize.
      :param df: gradient of the function to optimize.
      :param f_df: returns both the function to optimize and its gradient.
      :param duplicate_manager: logic to check for duplicate (always operates in the full space, context included)
      :param context_manager: If provided, x0 (and the optimizer) operates in the space without the context
      :param space: GPyOpt class design space.
      """
      x0 = np.atleast_2d(x0)
  
      ## --- Compute a new objective that inputs non context variables but that takes into account the values of the context ones.
      ## --- It does nothing if no context is passed
      problem = OptimizationWithContext(
          x0=x0, f=f, df=df, f_df=f_df, context_manager=context_manager
      )
  
      if context_manager:
          add_context = lambda x: context_manager._expand_vector(x)
      else:
          add_context = lambda x: x
  
      if (
          duplicate_manager
          and duplicate_manager.is_unzipped_x_duplicate(x0)
      ):
          raise ValueError(
              "The starting point of the optimizer cannot be a duplicate."
          )
  
      ## --- Optimize point
      optimized_x, _ = optimizer.optimize(
          problem.x0_nocontext,
          problem.f_nocontext,
          problem.df_nocontext,
          problem.f_df_nocontext,
      )
  
      ## --- Add context and round according to the type of variables of the design space
      suggested_x_with_context = add_context(optimized_x)
      suggested_x_with_context_rounded = space.round_optimum(
          suggested_x_with_context
      )
  
      ## --- Run duplicate_manager
      if (
          duplicate_manager
          and duplicate_manager.is_unzipped_x_duplicate(
              suggested_x_with_context_rounded
          )
      ):
          suggested_x, suggested_fx = x0, np.atleast_2d(f(x0))
      else:
          (
              suggested_x,
              suggested_fx,
          ) = suggested_x_with_context_rounded, f(
              suggested_x_with_context_rounded
          )
  
      return suggested_x, suggested_fx
  
imports: import numpy
  from ..core.errors import InvalidVariableNameError
label_desc: Use image node_id 1 for calling a global function with example usage: apply_optimizer(optimizer, x0, f, df, f_df, duplicate_manager, context_manager, space) and returns: suggested_x,  suggested_fx