optfunc provides differentiable PyTorch optfuncs and pytest-oriented helpers for evaluating first-order and second-order optimizers.

The package is published as optfuncs and imported as optfunc.

For CPU-only use:

pip install "optfuncs[torch-cpu]"

With uv in this repository:

uv sync --extra torch-cpu

Supported Torch extras:

Extra	Backend	Typical command
torch-cpu	CPU, Linux/macOS/Windows	uv sync --extra torch-cpu
torch-cu118	CUDA 11.8, Linux/Windows, PyTorch 2.7.x	uv sync --extra torch-cu118
torch-cu126	CUDA 12.6, Linux/Windows	uv sync --extra torch-cu126
torch-cu128	CUDA 12.8, Linux/Windows	uv sync --extra torch-cu128
torch-cu130	CUDA 13.0, Linux/Windows	uv sync --extra torch-cu130
torch-rocm	ROCm 7.1, Linux	uv sync --extra torch-rocm
torch-xpu	Intel XPU, Linux/Windows	uv sync --extra torch-xpu

Only choose one Torch extra at a time. The extras are configured as mutually exclusive in pyproject.toml.

Helper scripts:

# bash/zsh on Linux or macOS, and Git Bash/MSYS/Cygwin on Windows
./scripts/sync_torch_variant.sh cpu
./scripts/sync_torch_variant.sh cu130
./scripts/sync_torch_variant.sh rocm
./scripts/sync_torch_variant.sh xpu

# Windows PowerShell or PowerShell 7 on Windows/Linux/macOS
.\scripts\sync_torch_variant.ps1 cpu
.\scripts\sync_torch_variant.ps1 cu130
.\scripts\sync_torch_variant.ps1 rocm
.\scripts\sync_torch_variant.ps1 xpu

If Windows blocks local PowerShell scripts, run:

powershell -ExecutionPolicy Bypass -File .\scripts\sync_torch_variant.ps1 cu130

Platform notes:

• CPU works on Linux, macOS, and Windows.
• CUDA extras work on Linux and Windows.
• ROCm works on Linux.
• XPU works on Linux and Windows.
• macOS should use torch-cpu in this project configuration.

The backend indexes follow the official uv PyTorch guide and PyTorch install selector:

• https://docs.astral.sh/uv/guides/integration/pytorch/
• https://pytorch.org/get-started/locally/

The repository provides these built-in optfuncs:

Registry name	Class	Known minimizer
ackley	Ackley	all zeros
dixonprice	DixonPrice	recursive Dixon-Price optimum
griewank	Griewank	all zeros
levy	Levy	all ones
rastrigin	Rastrigin	all zeros
rosenbrock	Rosenbrock	all ones
rotatedhyperellipsoid	RotatedHyperEllipsoid	all zeros
schwefel	Schwefel	near 420.968746 in every coordinate
sphere	Sphere	all zeros
styblinskitang	StyblinskiTang	near -2.903534 in every coordinate
sumsquares	SumSquares	all zeros
trid	Trid	x_i = i * (d + 1 - i) with 1-based indexing
zakharov	Zakharov	all zeros

Use a class directly when you know which function you want:

import torch
from optfunc import Sphere

opt_func = Sphere(dim=8, dtype=torch.float64)
x = torch.zeros(8, dtype=torch.float64)

value = opt_func(x)
grad = opt_func.grad(x)
hessian = opt_func.hessian(x)
hvp = opt_func.hvp(x, torch.ones_like(x))
x_star = opt_func.global_minimizer()
distance = opt_func.distance_to_optimum(x)

Use OptFuncRegistry when a test should select an optfunc by name:

from optfunc import OptFuncRegistry

opt_func = OptFuncRegistry.create("rosenbrock", dim=4)
print(OptFuncRegistry.available())

Each optfunc uses the same conventions:

• input x is a 1-D PyTorch tensor with shape (dim,);
• output is a scalar tensor;
• grad, hessian, and hvp use PyTorch autograd unless a subclass provides a better implementation;
• global_minimizer() returns a known theoretical minimizer when available;
• distance_to_optimum(x) defaults to Euclidean distance to global_minimizer();
• project_to_bounds(x) clamps a point into the optfunc's documented search box.

The optimizer evaluation API lives in optfunc.testing. A standard test file has three parts:

1. Define or import an optimizer function.
2. Configure one or more OptimizerCase objects.
3. Assign make_optimizer_tests(...) to a pytest-visible name such as test_my_optimizer.

Run the file with:

uv run pytest tests/test_my_optimizer.py -q --tb=short --optfunc-report

Each OptimizerCase becomes an independent pytest item. If one case fails or raises an exception, pytest continues running the remaining cases. --optfunc-report prints a final serial summary with function gap, distance to the theoretical optimum, gradient norm, Hessian information, step count, and error messages. Do not combine --optfunc-report with pytest-xdist -n in v1.

OptimizerBudget describes the budget passed to the optimizer.

from optfunc.testing import OptimizerBudget

budget = OptimizerBudget(max_steps=500, lr=0.05)

Fields:

• max_steps: positive integer iteration limit.
• lr: positive learning-rate-like scalar. The test harness does not enforce how the optimizer uses it; your optimizer reads it from problem.budget.lr.

For torch.optim.Adam, a typical use is:

optimizer = torch.optim.Adam([x], lr=problem.budget.lr)
for step in range(problem.budget.max_steps):
    ...

ConvergenceTolerances decides whether a finished optimizer run passes.

from optfunc.testing import ConvergenceTolerances

tolerances = ConvergenceTolerances(
    value_gap=1e-8,
    x_distance=1e-4,
    grad_norm=1e-4,
    hessian_min_eig=0.0,
)

Fields:

• value_gap: maximum allowed absolute gap between final value and the known theoretical optimum value. Set to None to skip this check.
• x_distance: maximum allowed distance from final x to the known theoretical minimizer. Set to None to skip this check.
• grad_norm: maximum allowed Euclidean norm of the final gradient. Set to None to skip this check.
• hessian_min_eig: optional lower bound on the final Hessian's smallest eigenvalue. Set to None to skip this check.

The report still computes available metrics even when a tolerance is None; None only disables that pass/fail check.

OptimizerCase describes one pytest item.

from optfunc.testing import OptimizerCase
from optfunc.testing import OptimizerBudget, ConvergenceTolerances

case = OptimizerCase(
  opt_func="sphere",
  dim=8,
  budget=OptimizerBudget(max_steps=350, lr=0.05),
  tolerances=ConvergenceTolerances(value_gap=1e-8, x_distance=1e-4, grad_norm=1e-4),
  start="near_minimizer",
  start_radius=0.5,
  seed=0,
  hessian_max_dim=32,
)

Important fields:

• opt_func: registry name such as "sphere" or an already-created TorchOptFunction instance.
• dim: required when benchmark is a string.
• budget: OptimizerBudget passed to the optimizer through problem.budget.
• tolerances: ConvergenceTolerances used after the optimizer returns.
• case_id: optional pytest id; by default this is like sphere[8].
• x0: optional explicit initial point. If omitted, the harness builds one from start.
• start: "near_minimizer", "random", or "zeros".
• start_radius: offset size used by "near_minimizer".
• seed: random seed used by "random".
• device: optional torch device string, for example "cuda" or "cpu".
• dtype: torch dtype, default torch.float64.
• hessian_max_dim: largest dimension for dense Hessian report metrics. Larger cases skip dense Hessian metrics to avoid slow tests.

make_optimizer_tests converts an optimizer plus cases into a pytest test function.

from optfunc.testing import make_optimizer_tests

test_my_optimizer = make_optimizer_tests(
    optimizer=my_optimizer,
    cases=[case1, case2],
    name="test_my_optimizer",
)

Rules:

• Assign the returned function to a module-level variable whose name starts with test_, otherwise pytest will not collect it.
• optimizer must accept one OptimizationProblem argument.
• The optimizer may return either a final torch.Tensor or an OptimizerResult.
• Every case becomes an independent parametrized pytest item.

This example shows the recommended shape for a user-owned optimizer wrapper. The test harness does not hide torch.optim.Adam; the user function decides how to initialize Adam, how to use the budget, and what history to expose.

Create tests/test_torch_adam.py:

import torch

from optfunc.testing import (
  ConvergenceTolerances,
  OptimizerBudget,
  OptimizerCase,
  OptimizerResult,
  make_optimizer_tests,
  optimizer_adapter,
)


def scalar_item(value):
  return float(value.detach().cpu().item())


@optimizer_adapter(name="torch_adam")
def torch_adam(problem):
  x = problem.x0.detach().clone().requires_grad_(True)
  optimizer = torch.optim.Adam([x], lr=problem.budget.lr)
  history = []

  for step in range(1, problem.budget.max_steps + 1):
    optimizer.zero_grad(set_to_none=True)
    loss = problem.value(x)
    loss.backward()
    optimizer.step()

    with torch.no_grad():
      x.copy_(problem.project_to_bounds(x.detach()))

    if step % 25 == 0 or step == problem.budget.max_steps:
      x_now = x.detach()
      grad = problem.grad(x_now)
      history.append(
        {
          "step": step,
          "value": scalar_item(problem.value(x_now)),
          "grad_norm": scalar_item(torch.linalg.vector_norm(grad)),
          "x_norm": scalar_item(torch.linalg.vector_norm(x_now)),
        }
      )

  return OptimizerResult(
    final_x=x.detach().clone(),
    steps=problem.budget.max_steps,
    history=history,
  )


test_torch_adam = make_optimizer_tests(
  optimizer=torch_adam,
  cases=[
    OptimizerCase(
      opt_func="sphere",
      dim=8,
      budget=OptimizerBudget(max_steps=350, lr=0.05),
      tolerances=ConvergenceTolerances(
        value_gap=1e-8,
        x_distance=1e-4,
        grad_norm=1e-4,
      ),
      start="near_minimizer",
      start_radius=0.5,
    ),
    OptimizerCase(
      opt_func="rosenbrock",
      dim=4,
      budget=OptimizerBudget(max_steps=1200, lr=0.02),
      tolerances=ConvergenceTolerances(
        value_gap=5e-4,
        x_distance=5e-2,
        grad_norm=1e-2,
      ),
      start="near_minimizer",
      start_radius=0.25,
    ),
  ],
)

Run:

uv run pytest tests/test_torch_adam.py -q --tb=short --optfunc-report

The OptimizationProblem object passed into torch_adam exposes:

• problem.opt_func: the selected TorchOptFunction;
• problem.x0: the initial point for this case;
• problem.budget: the OptimizerBudget;
• problem.value(x): scalar objective value;
• problem.grad(x): gradient;
• problem.value_and_grad(x): objective and gradient;
• problem.hessian(x): dense Hessian;
• problem.hvp(x, v): Hessian-vector product;
• problem.project_to_bounds(x): clamp into the optfunc's bounds.

For second-order methods, call problem.hessian(x) or problem.hvp(x, v) inside the same optimizer wrapper and return the same OptimizerResult shape.

For smoke tests or examples, optfunc.testing.make_torch_adam() provides the same Adam loop as a convenience:

from optfunc.testing import make_torch_adam, make_optimizer_tests

test_adam = make_optimizer_tests(
    optimizer=make_torch_adam(),
    cases=[...],
)

For production optimizer tests, prefer writing the small wrapper yourself so the learning rate, projection, stopping rule, and history format are explicit in your test file.

uv sync --extra torch-cpu
uv run pytest -q --optfunc-report

On this repository's CUDA development path:

uv sync --extra torch-cu130
uv run pytest -q --optfunc-report

1. Update the package version in pyproject.toml, or run uv version <version> --frozen.
2. Create and push a Git tag named v<version>.
3. CNB will publish that tag to PyPI through the tag_push pipeline.

---

uv version z.x.y --frozen
rm -rf dist build src/*.egg-info
uv lock

git tag -a vz,x,y -m "Release vX.Y.Z"
git push origin vz,x,y

Optfunc definitions are adapted from SFU's optimization benchmark collection:

https://www.sfu.ca/~ssurjano/optimization.html