code: def optimize_acqf(
      acq_function: AcquisitionFunction,
      bounds: Tensor,
      q: int,
      num_restarts: int,
      raw_samples: Optional[int] = None,
      options: Optional[Dict[str, Union[bool, float, int, str]]] = None,
      inequality_constraints: Optional[
          List[Tuple[Tensor, Tensor, float]]
      ] = None,
      equality_constraints: Optional[
          List[Tuple[Tensor, Tensor, float]]
      ] = None,
      nonlinear_inequality_constraints: Optional[
          List[Tuple[Callable, bool]]
      ] = None,
      fixed_features: Optional[Dict[int, float]] = None,
      post_processing_func: Optional[Callable[[Tensor], Tensor]] = None,
      batch_initial_conditions: Optional[Tensor] = None,
      return_best_only: bool = True,
      gen_candidates: Optional[TGenCandidates] = None,
      sequential: bool = False,
      *,
      ic_generator: Optional[TGenInitialConditions] = None,
      timeout_sec: Optional[float] = None,
      return_full_tree: bool = False,
      retry_on_optimization_warning: bool = True,
      **ic_gen_kwargs: Any,
  ) -> Tuple[Tensor, Tensor]:
      r"""Generate a set of candidates via multi-start optimization.
  
      Args:
          acq_function: An AcquisitionFunction.
          bounds: A `2 x d` tensor of lower and upper bounds for each column of `X`
              (if inequality_constraints is provided, these bounds can be -inf and
              +inf, respectively).
          q: The number of candidates.
          num_restarts: The number of starting points for multistart acquisition
              function optimization.
          raw_samples: The number of samples for initialization. This is required
              if `batch_initial_conditions` is not specified.
          options: Options for candidate generation.
          inequality_constraints: A list of tuples (indices, coefficients, rhs),
              with each tuple encoding an inequality constraint of the form
              `\sum_i (X[indices[i]] * coefficients[i]) >= rhs`. `indices` and
              `coefficients` should be torch tensors. See the docstring of
              `make_scipy_linear_constraints` for an example. When q=1, or when
              applying the same constraint to each candidate in the batch
              (intra-point constraint), `indices` should be a 1-d tensor.
              For inter-point constraints, in which the constraint is applied to the
              whole batch of candidates, `indices` must be a 2-d tensor, where
              in each row `indices[i] =(k_i, l_i)` the first index `k_i` corresponds
              to the `k_i`-th element of the `q`-batch and the second index `l_i`
              corresponds to the `l_i`-th feature of that element.
          equality_constraints: A list of tuples (indices, coefficients, rhs),
              with each tuple encoding an equality constraint of the form
              `\sum_i (X[indices[i]] * coefficients[i]) = rhs`. See the docstring of
              `make_scipy_linear_constraints` for an example.
          nonlinear_inequality_constraints: A list of tuples representing the nonlinear
              inequality constraints. The first element in the tuple is a callable
              representing a constraint of the form `callable(x) >= 0`. In case of an
              intra-point constraint, `callable()`takes in an one-dimensional tensor of
              shape `d` and returns a scalar. In case of an inter-point constraint,
              `callable()` takes a two dimensional tensor of shape `q x d` and again
              returns a scalar. The second element is a boolean, indicating if it is an
              intra-point or inter-point constraint (`True` for intra-point. `False` for
              inter-point). For more information on intra-point vs inter-point
              constraints, see the docstring of the `inequality_constraints` argument to
              `optimize_acqf()`. The constraints will later be passed to the scipy
              solver. You need to pass in `batch_initial_conditions` in this case.
              Using non-linear inequality constraints also requires that `batch_limit`
              is set to 1, which will be done automatically if not specified in
              `options`.
          fixed_features: A map `{feature_index: value}` for features that
              should be fixed to a particular value during generation.
          post_processing_func: A function that post-processes an optimization
              result appropriately (i.e., according to `round-trip`
              transformations).
          batch_initial_conditions: A tensor to specify the initial conditions. Set
              this if you do not want to use default initialization strategy.
          return_best_only: If False, outputs the solutions corresponding to all
              random restart initializations of the optimization.
          gen_candidates: A callable for generating candidates (and their associated
              acquisition values) given a tensor of initial conditions and an
              acquisition function. Other common inputs include lower and upper bounds
              and a dictionary of options, but refer to the documentation of specific
              generation functions (e.g gen_candidates_scipy and gen_candidates_torch)
              for method-specific inputs. Default: `gen_candidates_scipy`
          sequential: If False, uses joint optimization, otherwise uses sequential
              optimization.
          ic_generator: Function for generating initial conditions. Not needed when
              `batch_initial_conditions` are provided. Defaults to
              `gen_one_shot_kg_initial_conditions` for `qKnowledgeGradient` acquisition
              functions and `gen_batch_initial_conditions` otherwise. Must be specified
              for nonlinear inequality constraints.
          timeout_sec: Max amount of time optimization can run for.
          return_full_tree:
          retry_on_optimization_warning: Whether to retry candidate generation with a new
              set of initial conditions when it fails with an `OptimizationWarning`.
          ic_gen_kwargs: Additional keyword arguments passed to function specified by
              `ic_generator`
  
      Returns:
          A two-element tuple containing
  
          - A tensor of generated candidates. The shape is
              -- `q x d` if `return_best_only` is True (default)
              -- `num_restarts x q x d` if `return_best_only` is False
          - a tensor of associated acquisition values. If `sequential=False`,
              this is a `(num_restarts)`-dim tensor of joint acquisition values
              (with explicit restart dimension if `return_best_only=False`). If
              `sequential=True`, this is a `q`-dim tensor of expected acquisition
              values conditional on having observed candidates `0,1,...,i-1`.
  
      Example:
          >>> # generate `q=2` candidates jointly using 20 random restarts
          >>> # and 512 raw samples
          >>> candidates, acq_value = optimize_acqf(qEI, bounds, 2, 20, 512)
  
          >>> generate `q=3` candidates sequentially using 15 random restarts
          >>> # and 256 raw samples
          >>> qEI = qExpectedImprovement(model, best_f=0.2)
          >>> bounds = torch.tensor([[0.], [1.]])
          >>> candidates, acq_value_list = optimize_acqf(
          >>>     qEI, bounds, 3, 15, 256, sequential=True
          >>> )
      """
      # using a default of None simplifies unit testing
      if gen_candidates is None:
          gen_candidates = gen_candidates_scipy
      opt_acqf_inputs = OptimizeAcqfInputs(
          acq_function=acq_function,
          bounds=bounds,
          q=q,
          num_restarts=num_restarts,
          raw_samples=raw_samples,
          options=options,
          inequality_constraints=inequality_constraints,
          equality_constraints=equality_constraints,
          nonlinear_inequality_constraints=nonlinear_inequality_constraints,
          fixed_features=fixed_features,
          post_processing_func=post_processing_func,
          batch_initial_conditions=batch_initial_conditions,
          return_best_only=return_best_only,
          gen_candidates=gen_candidates,
          sequential=sequential,
          ic_generator=ic_generator,
          timeout_sec=timeout_sec,
          return_full_tree=return_full_tree,
          retry_on_optimization_warning=retry_on_optimization_warning,
          ic_gen_kwargs=ic_gen_kwargs,
      )
      return _optimize_acqf(opt_acqf_inputs)
  
imports: from __future__ import annotations
  import dataclasses
  import warnings
  from typing import Any, Callable, Dict, List, Optional, Tuple, Union
  import torch
  from botorch.acquisition.acquisition import AcquisitionFunction, OneShotAcquisitionFunction
  from botorch.acquisition.knowledge_gradient import qKnowledgeGradient
  from botorch.acquisition.multi_objective.hypervolume_knowledge_gradient import qHypervolumeKnowledgeGradient
  from botorch.exceptions import InputDataError, UnsupportedError
  from botorch.exceptions.warnings import OptimizationWarning
  from botorch.generation.gen import gen_candidates_scipy, TGenCandidates
  from botorch.logging import logger
  from botorch.optim.initializers import gen_batch_initial_conditions, gen_one_shot_hvkg_initial_conditions, gen_one_shot_kg_initial_conditions, TGenInitialConditions
  from botorch.optim.stopping import ExpMAStoppingCriterion
  from botorch.optim.utils import _filter_kwargs
  from torch import Tensor
label_desc: Use image node_id 6 for calling a global function with example usage: optimize_acqf(acq_function, bounds, q, num_restarts, raw_samples, options, inequality_constraints, equality_constraints, nonlinear_inequality_constraints, fixed_features, post_processing_func, batch_initial_conditions, return_best_only, gen_candidates, sequential) and returns: _optimize_acqf