code: def gen_candidates_scipy(
      initial_conditions: Tensor,
      acquisition_function: AcquisitionFunction,
      lower_bounds: Optional[Union[float, Tensor]] = None,
      upper_bounds: Optional[Union[float, Tensor]] = 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,
      options: Optional[Dict[str, Any]] = None,
      fixed_features: Optional[Dict[int, Optional[float]]] = None,
      timeout_sec: Optional[float] = None,
  ) -> Tuple[Tensor, Tensor]:
      r"""Generate a set of candidates using `scipy.optimize.minimize`.
  
      Optimizes an acquisition function starting from a set of initial candidates
      using `scipy.optimize.minimize` via a numpy converter.
  
      Args:
          initial_conditions: Starting points for optimization, with shape
              (b) x q x d.
          acquisition_function: Acquisition function to be used.
          lower_bounds: Minimum values for each column of initial_conditions.
          upper_bounds: Maximum values for each column of initial_conditions.
          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`.
          equality 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`.
          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.
          options: Options used to control the optimization including "method"
              and "maxiter". Select method for `scipy.minimize` using the
              "method" key. By default uses L-BFGS-B for box-constrained problems
              and SLSQP if inequality or equality constraints are present. If
              `with_grad=False`, then we use a two-point finite difference estimate
              of the gradient.
          fixed_features: This is a dictionary of feature indices to values, where
              all generated candidates will have features fixed to these values.
              If the dictionary value is None, then that feature will just be
              fixed to the clamped value and not optimized. Assumes values to be
              compatible with lower_bounds and upper_bounds!
          timeout_sec: Timeout (in seconds) for `scipy.optimize.minimize` routine -
              if provided, optimization will stop after this many seconds and return
              the best solution found so far.
  
      Returns:
          2-element tuple containing
  
          - The set of generated candidates.
          - The acquisition value for each t-batch.
  
      Example:
          >>> qEI = qExpectedImprovement(model, best_f=0.2)
          >>> bounds = torch.tensor([[0., 0.], [1., 2.]])
          >>> Xinit = gen_batch_initial_conditions(
          >>>     qEI, bounds, q=3, num_restarts=25, raw_samples=500
          >>> )
          >>> batch_candidates, batch_acq_values = gen_candidates_scipy(
                  initial_conditions=Xinit,
                  acquisition_function=qEI,
                  lower_bounds=bounds[0],
                  upper_bounds=bounds[1],
              )
      """
      options = options or {}
      options = {**options, "maxiter": options.get("maxiter", 2000)}
  
      # if there are fixed features we may optimize over a domain of lower dimension
      reduced_domain = False
      if fixed_features:
          # if there are no constraints, things are straightforward
          if not (
              inequality_constraints
              or equality_constraints
              or nonlinear_inequality_constraints
          ):
              reduced_domain = True
          # if there are we need to make sure features are fixed to specific values
          else:
              reduced_domain = None not in fixed_features.values()
  
      if nonlinear_inequality_constraints:
          if not isinstance(nonlinear_inequality_constraints, list):
              raise ValueError(
                  "`nonlinear_inequality_constraints` must be a list of tuples, "
                  f"got {type(nonlinear_inequality_constraints)}."
              )
          nonlinear_inequality_constraints = (
              _convert_nonlinear_inequality_constraints(
                  nonlinear_inequality_constraints
              )
          )
  
      if reduced_domain:
          _no_fixed_features = _remove_fixed_features_from_optimization(
              fixed_features=fixed_features,
              acquisition_function=acquisition_function,
              initial_conditions=initial_conditions,
              lower_bounds=lower_bounds,
              upper_bounds=upper_bounds,
              inequality_constraints=inequality_constraints,
              equality_constraints=equality_constraints,
              nonlinear_inequality_constraints=nonlinear_inequality_constraints,
          )
          # call the routine with no fixed_features
          clamped_candidates, batch_acquisition = gen_candidates_scipy(
              initial_conditions=_no_fixed_features.initial_conditions,
              acquisition_function=_no_fixed_features.acquisition_function,
              lower_bounds=_no_fixed_features.lower_bounds,
              upper_bounds=_no_fixed_features.upper_bounds,
              inequality_constraints=_no_fixed_features.inequality_constraints,
              equality_constraints=_no_fixed_features.equality_constraints,
              nonlinear_inequality_constraints=_no_fixed_features.nonlinear_inequality_constraints,  # noqa: E501
              options=options,
              fixed_features=None,
              timeout_sec=timeout_sec,
          )
          clamped_candidates = (
              _no_fixed_features.acquisition_function._construct_X_full(
                  clamped_candidates
              )
          )
          return clamped_candidates, batch_acquisition
      clamped_candidates = columnwise_clamp(
          X=initial_conditions, lower=lower_bounds, upper=upper_bounds
      )
  
      shapeX = clamped_candidates.shape
      x0 = clamped_candidates.view(-1)
      bounds = make_scipy_bounds(
          X=initial_conditions,
          lower_bounds=lower_bounds,
          upper_bounds=upper_bounds,
      )
      constraints = make_scipy_linear_constraints(
          shapeX=shapeX,
          inequality_constraints=inequality_constraints,
          equality_constraints=equality_constraints,
      )
  
      with_grad = options.get("with_grad", True)
      if with_grad:
  
          def f_np_wrapper(x: np.ndarray, f: Callable):
              """Given a torch callable, compute value + grad given a numpy array."""
              if np.isnan(x).any():
                  raise RuntimeError(
                      f"{np.isnan(x).sum()} elements of the {x.size} element array "
                      f"`x` are NaN."
                  )
              X = (
                  torch.from_numpy(x)
                  .to(initial_conditions)
                  .view(shapeX)
                  .contiguous()
                  .requires_grad_(True)
              )
              X_fix = fix_features(X, fixed_features=fixed_features)
              loss = f(X_fix).sum()
              # compute gradient w.r.t. the inputs (does not accumulate in leaves)
              gradf = _arrayify(
                  torch.autograd.grad(loss, X)[0].contiguous().view(-1)
              )
              if np.isnan(gradf).any():
                  msg = (
                      f"{np.isnan(gradf).sum()} elements of the {x.size} element "
                      "gradient array `gradf` are NaN. "
                      "This often indicates numerical issues."
                  )
                  if initial_conditions.dtype != torch.double:
                      msg += " Consider using `dtype=torch.double`."
                  raise RuntimeError(msg)
              fval = loss.item()
              return fval, gradf
  
      else:
  
          def f_np_wrapper(x: np.ndarray, f: Callable):
              X = (
                  torch.from_numpy(x)
                  .to(initial_conditions)
                  .view(shapeX)
                  .contiguous()
              )
              with torch.no_grad():
                  X_fix = fix_features(
                      X=X, fixed_features=fixed_features
                  )
                  loss = f(X_fix).sum()
              fval = loss.item()
              return fval
  
      if nonlinear_inequality_constraints:
          # Make sure `batch_limit` is 1 for now.
          if not (
              len(shapeX) == 3 and shapeX[:2] == torch.Size([1, 1])
          ):
              raise ValueError(
                  "`batch_limit` must be 1 when non-linear inequality constraints "
                  "are given."
              )
          constraints += make_scipy_nonlinear_inequality_constraints(
              nonlinear_inequality_constraints=nonlinear_inequality_constraints,
              f_np_wrapper=f_np_wrapper,
              x0=x0,
              shapeX=shapeX,
          )
      x0 = _arrayify(x0)
  
      def f(x):
          return -acquisition_function(x)
  
      res = minimize_with_timeout(
          fun=f_np_wrapper,
          args=(f,),
          x0=x0,
          method=options.get(
              "method", "SLSQP" if constraints else "L-BFGS-B"
          ),
          jac=with_grad,
          bounds=bounds,
          constraints=constraints,
          callback=options.get("callback", None),
          options={
              k: v
              for k, v in options.items()
              if k not in ["method", "callback", "with_grad"]
          },
          timeout_sec=timeout_sec,
      )
      _process_scipy_result(res=res, options=options)
  
      candidates = fix_features(
          X=torch.from_numpy(res.x)
          .to(initial_conditions)
          .reshape(shapeX),
          fixed_features=fixed_features,
      )
  
      # SLSQP sometimes fails in the line search or may just fail to find a feasible
      # candidate in which case we just return the starting point. This happens rarely,
      # so it shouldn't be an issue given enough restarts.
      if nonlinear_inequality_constraints:
          for con, is_intrapoint in nonlinear_inequality_constraints:
              if not nonlinear_constraint_is_feasible(
                  con, is_intrapoint=is_intrapoint, x=candidates
              ):
                  candidates = (
                      torch.from_numpy(x0)
                      .to(candidates)
                      .reshape(shapeX)
                  )
                  warnings.warn(
                      "SLSQP failed to converge to a solution the satisfies the "
                      "non-linear constraints. Returning the feasible starting point."
                  )
                  break
  
      clamped_candidates = columnwise_clamp(
          X=candidates,
          lower=lower_bounds,
          upper=upper_bounds,
          raise_on_violation=True,
      )
      with torch.no_grad():
          batch_acquisition = acquisition_function(clamped_candidates)
  
      return clamped_candidates, batch_acquisition
  
imports: from __future__ import annotations
  import time
  import warnings
  from functools import partial
  from typing import Any, Callable, Dict, List, NoReturn, Optional, Tuple, Type, Union
  import numpy
  import torch
  from botorch.acquisition import AcquisitionFunction
  from botorch.exceptions.warnings import OptimizationWarning
  from botorch.generation.utils import _convert_nonlinear_inequality_constraints, _remove_fixed_features_from_optimization
  from botorch.logging import _get_logger
  from botorch.optim.parameter_constraints import _arrayify, make_scipy_bounds, make_scipy_linear_constraints, make_scipy_nonlinear_inequality_constraints, nonlinear_constraint_is_feasible
  from botorch.optim.stopping import ExpMAStoppingCriterion
  from botorch.optim.utils import columnwise_clamp, fix_features
  from botorch.optim.utils.timeout import minimize_with_timeout
  from scipy.optimize import OptimizeResult
  from torch import Tensor
  from torch.optim import Optimizer
label_desc: Use image node_id 1 for calling a global function with example usage: gen_candidates_scipy(initial_conditions, acquisition_function, lower_bounds, upper_bounds, inequality_constraints, equality_constraints, nonlinear_inequality_constraints, options, fixed_features, timeout_sec) and returns: clamped_candidates,  batch_acquisition, clamped_candidates,  batch_acquisition, unknown, fval,  gradf, fval