Getting started

Install

pip install -e ".[numpy]"     # core + NumPy backend
pip install -e ".[dev]"       # full dev environment

CUDA dependencies are user-managed because the CuPy wheel must match the local CUDA toolkit. Install the appropriate CuPy package and cuDSS runtime first, then install the optional nvmath bindings:

# Example only: choose the CuPy package matching your installed CUDA toolkit.
pip install cupy-cuda12x
pip install -e ".[sparse-cuda]"

If nvmath or cuDSS cannot be loaded, the CuPy sparse adapter remains available through its solve-only cupyx.scipy.sparse.linalg.spsolve fallback. Sparse KKT inertia requires a working cuDSS runtime.

Define a problem

Subclass ipax.Problem. Only n_vars and objective are required.

import numpy as np
import ipax

class Rosenbrock(ipax.Problem):
    @property
    def n_vars(self) -> int:
        return 2

    def objective(self, x):
        return 100.0 * (x[1] - x[0] ** 2) ** 2 + (1 - x[0]) ** 2

res = ipax.solve(Rosenbrock(), x0=np.array([-1.2, 1.0]))
print(res.status, res.x)

Switch backends by switching the array type — pass a torch.Tensor as x0 and the entire solve runs in PyTorch.

Supplying derivatives

Override any of gradient, eq_constraints/eq_jacobian, ineq_constraints/ineq_jacobian, lagrangian_hessian. Anything you omit is resolved automatically (analytic → autodiff → finite-difference; Hessian → autodiff-HVP → L-BFGS). The chosen source is reported in res.derivative_sources.

Linear vs nonlinear constraints

Declare linear constraints separately via linear_eq() / linear_ineq(): their Jacobian is constant and assembled once, and they contribute no Hessian term — a real performance lever at scale.