diff --git a/botorch/acquisition/multi_objective/utils.py b/botorch/acquisition/multi_objective/utils.py
index cca67ad55e..ca45c869e6 100644
--- a/botorch/acquisition/multi_objective/utils.py
+++ b/botorch/acquisition/multi_objective/utils.py
@@ -10,7 +10,6 @@
 
 from __future__ import annotations
 
-import math
 import warnings
 from collections.abc import Callable
 from math import ceil
@@ -18,16 +17,12 @@
 
 import torch
 from botorch.acquisition import monte_carlo  # noqa F401
-from botorch.acquisition.multi_objective.objective import (
-    IdentityMCMultiOutputObjective,
-    MCMultiOutputObjective,
-)
+from botorch.acquisition.multi_objective.objective import MCMultiOutputObjective
+from botorch.acquisition.utils import _prune_inferior_shared_processing
 from botorch.exceptions.errors import UnsupportedError
 from botorch.exceptions.warnings import BotorchWarning
 from botorch.models.deterministic import GenericDeterministicModel
-from botorch.models.fully_bayesian import MCMC_DIM
 from botorch.models.model import Model
-from botorch.sampling.get_sampler import get_sampler
 from botorch.sampling.pathwise.posterior_samplers import get_matheron_path_model
 from botorch.utils.multi_objective.box_decompositions.box_decomposition import (
     BoxDecomposition,
@@ -39,9 +34,8 @@
     DominatedPartitioning,
 )
 from botorch.utils.multi_objective.pareto import is_non_dominated
-from botorch.utils.objective import compute_feasibility_indicator
 from botorch.utils.sampling import draw_sobol_samples
-from botorch.utils.transforms import is_ensemble
+from pyre_extensions import assert_is_instance
 from torch import Tensor
 
 
@@ -115,40 +109,14 @@ def prune_inferior_points_multi_objective(
         with `N_nz` the number of points in `X` that have non-zero (empirical,
         under `num_samples` samples) probability of being pareto optimal.
     """
-    if marginalize_dim is None and is_ensemble(model):
-        # TODO: Properly deal with marginalizing fully Bayesian models
-        marginalize_dim = MCMC_DIM
-
-    if X.ndim > 2:
-        # TODO: support batched inputs (req. dealing with ragged tensors)
-        raise UnsupportedError(
-            "Batched inputs `X` are currently unsupported by "
-            "prune_inferior_points_multi_objective"
-        )
-    if X.size(-2) == 0:
-        raise ValueError("X must have at least one point.")
-    if max_frac <= 0 or max_frac > 1.0:
-        raise ValueError(f"max_frac must take values in (0, 1], is {max_frac}")
-    max_points = math.ceil(max_frac * X.size(-2))
-    with torch.no_grad():
-        posterior = model.posterior(X=X)
-    sampler = get_sampler(posterior, sample_shape=torch.Size([num_samples]))
-    samples = sampler(posterior)
-    if objective is None:
-        objective = IdentityMCMultiOutputObjective()
-    obj_vals = objective(samples, X=X)
-    if obj_vals.ndim > 3:
-        if obj_vals.ndim == 4 and marginalize_dim is not None:
-            obj_vals = obj_vals.mean(dim=marginalize_dim)
-        else:
-            # TODO: support batched inputs (req. dealing with ragged tensors)
-            raise UnsupportedError(
-                "Models with multiple batch dims are currently unsupported by"
-                " prune_inferior_points_multi_objective."
-            )
-    infeas = ~compute_feasibility_indicator(
+    max_points, obj_vals, infeas = _prune_inferior_shared_processing(
+        model=model,
+        X=X,
+        is_moo=True,
+        objective=objective,
         constraints=constraints,
-        samples=samples,
+        num_samples=num_samples,
+        max_frac=max_frac,
         marginalize_dim=marginalize_dim,
     )
     if infeas.any():
@@ -168,9 +136,9 @@ def prune_inferior_points_multi_objective(
 
 def compute_sample_box_decomposition(
     pareto_fronts: Tensor,
-    partitioning: BoxDecomposition = DominatedPartitioning,
+    partitioning: type[BoxDecomposition] = DominatedPartitioning,
     maximize: bool = True,
-    num_constraints: int | None = 0,
+    num_constraints: int = 0,
 ) -> Tensor:
     r"""Computes the box decomposition associated with some sampled optimal
     objectives. This also supports the single-objective and constrained optimization
@@ -195,7 +163,10 @@ def compute_sample_box_decomposition(
         the hyper-rectangles. The number `J` is the smallest number of boxes needed
         to partition all the Pareto samples.
     """
-    tkwargs = {"dtype": pareto_fronts.dtype, "device": pareto_fronts.device}
+    tkwargs: dict[str, Any] = {
+        "dtype": pareto_fronts.dtype,
+        "device": pareto_fronts.device,
+    }
     # We will later compute `norm.log_prob(NEG_INF)`, this is `-inf` if `NEG_INF` is
     # too small.
     NEG_INF = -1e10
@@ -214,16 +185,18 @@ def compute_sample_box_decomposition(
 
     if M == 1:
         # Only consider a Pareto front with one element.
-        extreme_values = weight * torch.max(weight * pareto_fronts, dim=-2).values
+        extreme_values = assert_is_instance(
+            weight * torch.max(weight * pareto_fronts, dim=-2).values, Tensor
+        )
         ref_point = weight * ref_point.expand(extreme_values.shape)
 
         if maximize:
             hypercell_bounds = torch.stack(
-                [ref_point, extreme_values], axis=-2
+                [ref_point, extreme_values], dim=-2
             ).unsqueeze(-1)
         else:
             hypercell_bounds = torch.stack(
-                [extreme_values, ref_point], axis=-2
+                [extreme_values, ref_point], dim=-2
             ).unsqueeze(-1)
     else:
         bd_list = []
@@ -244,9 +217,7 @@ def compute_sample_box_decomposition(
     # Add an extra box for the inequality constraint.
     if K > 0:
         # `num_pareto_samples x 2 x (J - 1) x K`
-        feasible_boxes = torch.zeros(
-            hypercell_bounds.shape[:-1] + torch.Size([K]), **tkwargs
-        )
+        feasible_boxes = torch.zeros(hypercell_bounds.shape[:-1] + (K,), **tkwargs)
 
         feasible_boxes[..., 0, :, :] = NEG_INF
         # `num_pareto_samples x 2 x (J - 1) x (M + K)`
@@ -254,7 +225,7 @@ def compute_sample_box_decomposition(
 
         # `num_pareto_samples x 2 x 1 x (M + K)`
         infeasible_box = torch.zeros(
-            hypercell_bounds.shape[:-2] + torch.Size([1, M + K]), **tkwargs
+            hypercell_bounds.shape[:-2] + (1, M + K), **tkwargs
         )
         infeasible_box[..., 1, :, M:] = -NEG_INF
         infeasible_box[..., 0, :, 0:M] = NEG_INF
@@ -292,11 +263,12 @@ def random_search_optimizer(
         - A `num_points x M`-dim Tensor containing the collection of optimal
             objectives.
     """
-    tkwargs = {"dtype": bounds.dtype, "device": bounds.device}
+    tkwargs: dict[str, Any] = {"dtype": bounds.dtype, "device": bounds.device}
     weight = 1.0 if maximize else -1.0
     optimal_inputs = torch.tensor([], **tkwargs)
     optimal_outputs = torch.tensor([], **tkwargs)
     num_tries = 0
+    num_found = 0
     ratio = 2
     while ratio > 1 and num_tries < max_tries:
         X = draw_sobol_samples(bounds=bounds, n=pop_size, q=1).squeeze(-2)
diff --git a/botorch/acquisition/utils.py b/botorch/acquisition/utils.py
index d486629b76..a930488680 100644
--- a/botorch/acquisition/utils.py
+++ b/botorch/acquisition/utils.py
@@ -15,7 +15,6 @@
 
 import torch
 from botorch.acquisition.objective import (
-    IdentityMCObjective,
     MCAcquisitionObjective,
     PosteriorTransform,
     ScalarizedPosteriorTransform,
@@ -34,6 +33,7 @@
 from botorch.utils.sampling import optimize_posterior_samples
 from botorch.utils.transforms import is_ensemble, normalize_indices
 from gpytorch.models import GP
+from pyre_extensions import none_throws
 from torch import Tensor
 
 
@@ -244,6 +244,76 @@ def objective(Y: Tensor, X: Tensor | None = None):
     return -(lb.clamp_max(0.0))
 
 
+def _prune_inferior_shared_processing(
+    model: Model,
+    X: Tensor,
+    is_moo: bool,
+    objective: MCAcquisitionObjective | None = None,
+    posterior_transform: PosteriorTransform | None = None,
+    constraints: list[Callable[[Tensor], Tensor]] | None = None,
+    num_samples: int = 2048,
+    max_frac: float = 1.0,
+    sampler: MCSampler | None = None,
+    marginalize_dim: int | None = None,
+) -> tuple[int, Tensor, Tensor]:
+    r"""Shared data processing for `prune_inferior_points` and
+    `prune_inferior_points_multi_objective`.
+
+    Returns:
+        - max_points: The maximum number of points to keep.
+        - obj_vals: The objective values of the points in `X`.
+        - infeas: A boolean tensor indicating feasibility of `X`.
+    """
+    func_name = (
+        "prune_inferior_points_multi_objective" if is_moo else "prune_inferior_points"
+    )
+    if marginalize_dim is None and is_ensemble(model):
+        marginalize_dim = MCMC_DIM
+
+    if X.ndim > 2:
+        raise UnsupportedError(
+            f"Batched inputs `X` are currently unsupported by `{func_name}`"
+        )
+    if X.size(-2) == 0:
+        raise ValueError("X must have at least one point.")
+    if max_frac <= 0 or max_frac > 1.0:
+        raise ValueError(f"max_frac must take values in (0, 1], is {max_frac}")
+    max_points = math.ceil(max_frac * X.size(-2))
+    with torch.no_grad():
+        posterior = model.posterior(X=X, posterior_transform=posterior_transform)
+    if sampler is None:
+        sampler = get_sampler(
+            posterior=posterior, sample_shape=torch.Size([num_samples])
+        )
+    samples = sampler(posterior)
+    if objective is not None:
+        obj_vals = objective(samples=samples, X=X)
+    elif is_moo:
+        obj_vals = samples
+    else:
+        obj_vals = samples.squeeze(-1)
+    if obj_vals.ndim > (2 + is_moo):
+        if obj_vals.ndim == (3 + is_moo) and marginalize_dim is not None:
+            if marginalize_dim < 0:
+                # Update `marginalize_dim` to be positive while accounting for
+                # removal of output dimension in SOO.
+                marginalize_dim = (not is_moo) + none_throws(
+                    normalize_indices([marginalize_dim], d=obj_vals.ndim)
+                )[0]
+            obj_vals = obj_vals.mean(dim=marginalize_dim)
+        else:
+            raise UnsupportedError(
+                "Models with multiple batch dims are currently unsupported by "
+                f"`{func_name}`."
+            )
+    infeas = ~compute_feasibility_indicator(
+        constraints=constraints,
+        samples=samples,
+        marginalize_dim=marginalize_dim,
+    )
+    return max_points, obj_vals, infeas
+
+
 def prune_inferior_points(
     model: Model,
     X: Tensor,
@@ -292,48 +362,16 @@ def prune_inferior_points(
         with `N_nz` the number of points in `X` that have non-zero (empirical,
         under `num_samples` samples) probability of being the best point.
     """
-    if marginalize_dim is None and is_ensemble(model):
-        # TODO: Properly deal with marginalizing fully Bayesian models
-        marginalize_dim = MCMC_DIM
-
-    if X.ndim > 2:
-        # TODO: support batched inputs (req. dealing with ragged tensors)
-        raise UnsupportedError(
-            "Batched inputs `X` are currently unsupported by prune_inferior_points"
-        )
-    if X.size(-2) == 0:
-        raise ValueError("X must have at least one point.")
-    if max_frac <= 0 or max_frac > 1.0:
-        raise ValueError(f"max_frac must take values in (0, 1], is {max_frac}")
-    max_points = math.ceil(max_frac * X.size(-2))
-    with torch.no_grad():
-        posterior = model.posterior(X=X, posterior_transform=posterior_transform)
-    if sampler is None:
-        sampler = get_sampler(
-            posterior=posterior, sample_shape=torch.Size([num_samples])
-        )
-    samples = sampler(posterior)
-    if objective is None:
-        objective = IdentityMCObjective()
-    obj_vals = objective(samples, X=X)
-    if obj_vals.ndim > 2:
-        if obj_vals.ndim == 3 and marginalize_dim is not None:
-            if marginalize_dim < 0:
-                # we do this again in compute_feasibility_indicator, but that will
-                # have no effect since marginalize_dim will be non-negative
-                marginalize_dim = (
-                    1 + normalize_indices([marginalize_dim], d=obj_vals.ndim)[0]
-                )
-            obj_vals = obj_vals.mean(dim=marginalize_dim)
-        else:
-            # TODO: support batched inputs (req. dealing with ragged tensors)
-            raise UnsupportedError(
-                "Models with multiple batch dims are currently unsupported by"
-                " prune_inferior_points."
-            )
-    infeas = ~compute_feasibility_indicator(
+    max_points, obj_vals, infeas = _prune_inferior_shared_processing(
+        model=model,
+        X=X,
+        is_moo=False,
+        objective=objective,
+        posterior_transform=posterior_transform,
         constraints=constraints,
-        samples=samples,
+        num_samples=num_samples,
+        max_frac=max_frac,
+        sampler=sampler,
         marginalize_dim=marginalize_dim,
     )
     if infeas.any():
diff --git a/botorch/generation/gen.py b/botorch/generation/gen.py
index 6e6e047f05..0d70681fd5 100644
--- a/botorch/generation/gen.py
+++ b/botorch/generation/gen.py
@@ -22,10 +22,7 @@
 from botorch.acquisition import AcquisitionFunction
 from botorch.exceptions.errors import OptimizationGradientError
 from botorch.exceptions.warnings import OptimizationWarning
-from botorch.generation.utils import (
-    _convert_nonlinear_inequality_constraints,
-    _remove_fixed_features_from_optimization,
-)
+from botorch.generation.utils import _remove_fixed_features_from_optimization
 from botorch.logging import logger
 from botorch.optim.parameter_constraints import (
     _arrayify,
@@ -136,16 +133,6 @@ def gen_candidates_scipy(
         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,
diff --git a/botorch/generation/utils.py b/botorch/generation/utils.py
index 44bba19c24..a6cbaa67ef 100644
--- a/botorch/generation/utils.py
+++ b/botorch/generation/utils.py
@@ -6,12 +6,10 @@
 
 from __future__ import annotations
 
-import warnings
 from collections.abc import Callable
 from dataclasses import dataclass
 
 import torch
-
 from botorch.acquisition import AcquisitionFunction, FixedFeatureAcquisitionFunction
 from botorch.optim.parameter_constraints import (
     _generate_unfixed_lin_constraints,
@@ -20,34 +18,6 @@
 from torch import Tensor
 
 
-def _convert_nonlinear_inequality_constraints(
-    nonlinear_inequality_constraints: list[Callable | tuple[Callable, bool]],
-) -> list[tuple[Callable, bool]]:
-    """Convert legacy defintions of nonlinear inequality constraints into the new
-    format. Assumes intra-point constraints.
-    """
-    nlcs = []
-    legacy = False
-    # return nonlinear_inequality_constraints
-    for nlc in nonlinear_inequality_constraints:
-        if callable(nlc):
-            # old style --> convert
-            nlcs.append((nlc, True))
-            legacy = True
-        else:
-            nlcs.append(nlc)
-    if legacy:
-        warnings.warn(
-            "The `nonlinear_inequality_constraints` argument is expected "
-            "take a list of tuples. Passing a list of callables "
-            "will result in an error in future versions.",
-            DeprecationWarning,
-            stacklevel=3,
-        )
-
-    return nlcs
-
-
 def _flip_sub_unique(x: Tensor, k: int) -> Tensor:
     """Get the first k unique elements of a single-dimensional tensor, traversing the
     tensor from the back.
diff --git a/botorch/utils/datasets.py b/botorch/utils/datasets.py
index f11f5c80e7..1007be8c0a 100644
--- a/botorch/utils/datasets.py
+++ b/botorch/utils/datasets.py
@@ -8,7 +8,6 @@
 
 from __future__ import annotations
 
-import warnings
 from typing import Any
 
 import torch
@@ -149,39 +148,6 @@ def __eq__(self, other: Any) -> bool:
         )
 
 
-class FixedNoiseDataset(SupervisedDataset):
-    r"""A SupervisedDataset with an additional field `Yvar` that stipulates
-    observations variances so that `Y[i] ~ N(f(X[i]), Yvar[i])`.
-
-    NOTE: This is deprecated. Use `SupervisedDataset` instead.
-    Will be removed in a future release (~v0.11).
-    """
-
-    def __init__(
-        self,
-        X: BotorchContainer | Tensor,
-        Y: BotorchContainer | Tensor,
-        Yvar: BotorchContainer | Tensor,
-        feature_names: list[str],
-        outcome_names: list[str],
-        validate_init: bool = True,
-    ) -> None:
-        r"""Initialize a `FixedNoiseDataset` -- deprecated!"""
-        warnings.warn(
-            "`FixedNoiseDataset` is deprecated. Use `SupervisedDataset` instead.",
-            DeprecationWarning,
-            stacklevel=2,
-        )
-        super().__init__(
-            X=X,
-            Y=Y,
-            feature_names=feature_names,
-            outcome_names=outcome_names,
-            Yvar=Yvar,
-            validate_init=validate_init,
-        )
-
-
 class RankingDataset(SupervisedDataset):
     r"""A SupervisedDataset whose labelled pairs `(x, y)` consist of m-ary combinations
     `x ∈ Z^{m}` of elements from a ground set `Z = (z_1, ...)` and ranking vectors
diff --git a/botorch/utils/testing.py b/botorch/utils/testing.py
index 5f5b6a6df1..3c468f9e6b 100644
--- a/botorch/utils/testing.py
+++ b/botorch/utils/testing.py
@@ -17,7 +17,11 @@
 
 import torch
 from botorch.acquisition.objective import PosteriorTransform
-from botorch.exceptions.warnings import BotorchTensorDimensionWarning, InputDataWarning
+from botorch.exceptions.warnings import (
+    BotorchTensorDimensionWarning,
+    InputDataWarning,
+    NumericsWarning,
+)
 from botorch.models.model import FantasizeMixin, Model
 from botorch.posteriors.gpytorch import GPyTorchPosterior
 from botorch.posteriors.posterior import Posterior
@@ -68,6 +72,16 @@ def setUp(self, suppress_input_warnings: bool = True) -> None:
                 message=r"Data \(input features\) is not",
                 category=InputDataWarning,
             )
+            warnings.filterwarnings(
+                "ignore",
+                message="has known numerical issues",
+                category=NumericsWarning,
+            )
+            warnings.filterwarnings(
+                "ignore",
+                message="Model converter code is deprecated",
+                category=DeprecationWarning,
+            )
 
     def assertAllClose(
         self,
diff --git a/test/acquisition/test_utils.py b/test/acquisition/test_utils.py
index 7e4718150e..b8115ba0af 100644
--- a/test/acquisition/test_utils.py
+++ b/test/acquisition/test_utils.py
@@ -9,7 +9,6 @@
 from unittest.mock import patch
 
 import torch
-
 from botorch.acquisition.objective import (
     ExpectationPosteriorTransform,
     GenericMCObjective,
@@ -34,7 +33,6 @@
     UnsupportedError,
 )
 from botorch.models import SingleTaskGP
-
 from botorch.utils.testing import BotorchTestCase, MockModel, MockPosterior
 from gpytorch.distributions import MultivariateNormal
 
diff --git a/test/generation/test_utils.py b/test/generation/test_utils.py
index c5fd0e7c83..6c6176a2b9 100644
--- a/test/generation/test_utils.py
+++ b/test/generation/test_utils.py
@@ -12,7 +12,6 @@
 
 from botorch.acquisition import FixedFeatureAcquisitionFunction
 from botorch.generation.utils import (
-    _convert_nonlinear_inequality_constraints,
     _flip_sub_unique,
     _remove_fixed_features_from_optimization,
 )
@@ -20,27 +19,6 @@
 
 
 class TestGenerationUtils(BotorchTestCase):
-    def test_convert_nonlinear_inequality_constraints(self):
-        def nlc(x):
-            return x[..., 2]
-
-        def nlc2(x):
-            return x[..., 3]
-
-        nlcs = [nlc]
-        with self.assertWarns(DeprecationWarning):
-            new_nlcs = _convert_nonlinear_inequality_constraints(nlcs)
-        self.assertEqual(new_nlcs, [(nlc, True)])
-
-        nlcs = [(nlc, False)]
-        new_nlcs = _convert_nonlinear_inequality_constraints(nlcs)
-        self.assertEqual(new_nlcs, [(nlc, False)])
-
-        nlcs = [(nlc, False), nlc2]
-        with self.assertWarns(DeprecationWarning):
-            new_nlcs = _convert_nonlinear_inequality_constraints(nlcs)
-        self.assertEqual(new_nlcs, [(nlc, False), (nlc2, True)])
-
     def test_flip_sub_unique(self):
         for dtype in (torch.float, torch.double):
             tkwargs = {"device": self.device, "dtype": dtype}
diff --git a/test/optim/test_optimize.py b/test/optim/test_optimize.py
index 4da68e9e3e..029fbb8c77 100644
--- a/test/optim/test_optimize.py
+++ b/test/optim/test_optimize.py
@@ -1083,20 +1083,6 @@ def nlc4(x):
                 )
                 self.assertEqual(candidates.size(), torch.Size([1, 3]))
 
-            # Constraints must be passed in as lists
-            with self.assertRaisesRegex(
-                ValueError,
-                "`nonlinear_inequality_constraints` must be a list of tuples, "
-                "got <class 'function'>.",
-            ):
-                optimize_acqf(
-                    acq_function=mock_acq_function,
-                    bounds=bounds,
-                    q=1,
-                    nonlinear_inequality_constraints=nlc1,
-                    num_restarts=num_restarts,
-                    batch_initial_conditions=batch_initial_conditions,
-                )
             # batch_initial_conditions must be feasible
             with self.assertRaisesRegex(
                 ValueError,
diff --git a/test/utils/test_datasets.py b/test/utils/test_datasets.py
index 22d8c24a50..de741c1a60 100644
--- a/test/utils/test_datasets.py
+++ b/test/utils/test_datasets.py
@@ -10,7 +10,6 @@
 from botorch.utils.containers import DenseContainer, SliceContainer
 from botorch.utils.datasets import (
     ContextualDataset,
-    FixedNoiseDataset,
     MultiTaskDataset,
     RankingDataset,
     SupervisedDataset,
@@ -129,7 +128,7 @@ def test_fixedNoise(self):
         Yvar = rand(3, 1)
         feature_names = ["x1", "x2"]
         outcome_names = ["y"]
-        dataset = FixedNoiseDataset(
+        dataset = SupervisedDataset(
             X=X,
             Y=Y,
             Yvar=Yvar,
@@ -142,17 +141,6 @@ def test_fixedNoise(self):
         self.assertEqual(dataset.feature_names, feature_names)
         self.assertEqual(dataset.outcome_names, outcome_names)
 
-        with self.assertRaisesRegex(
-            ValueError, "`Y` and `Yvar`"
-        ), self.assertWarnsRegex(DeprecationWarning, "SupervisedDataset"):
-            FixedNoiseDataset(
-                X=X,
-                Y=Y,
-                Yvar=Yvar.squeeze(),
-                feature_names=feature_names,
-                outcome_names=outcome_names,
-            )
-
     def test_ranking(self):
         # Test `_validate`
         X_val = rand(16, 2)