mincon

Nonlinear constrained optimization with a Rust solver and a simple Python API. Supply your objective, starting point and constraints. Derivative estimation, scaling and solver configuration have automatic defaults.

Experimental 0.1 release. This is research software under active development, not a completed or proven superior replacement for MATLAB's fmincon. It computes local solutions; it does not guarantee global minima.

Install

python -m pip install mincon

Prebuilt wheels target standard CPython on Windows x86_64 and Linux x86_64. NumPy is installed automatically. On platforms without a matching wheel, pip builds from source and requires Rust 1.83 or newer and a C/C++ toolchain. macOS wheels and broader runtime coverage remain release work.

Familiar fmincon inputs

from mincon import fmincon

# Closest point to (1, 1), subject to x[0] + x[1] <= 1.
result = fmincon(
    lambda x: ((x - 1)**2).sum(),
    [0., 0.],
    nonlcon=lambda x: ([x.sum() - 1], []),
)
print(result.x)       # approximately [0.5, 0.5]
print(result.fun)     # approximately 0.5
print(result.success, result.message)

No gradients, Hessians, algorithm selection or tolerance settings are required. Optional constraint arguments use MATLAB's conventions:

For example, fmincon(fun, x0, A=[[1, 1]], b=[1], lb=0) uses only linear constraints and bounds. The result is a Python object, not MATLAB's output tuple. result.multipliers groups multipliers with MATLAB's signs. Options use Python names such as options={"maxiter": 500}, not MATLAB option names.

SciPy-style inputs

from mincon import minimize

result = minimize(
    lambda x: ((x - 1)**2).sum(),
    [0., 0.],
    constraints={"type": "ineq", "fun": lambda x: 1 - x.sum()},
)

Sign convention: minimize inequalities mean fun(x) >= 0; fmincon nonlinear inequalities mean c(x) <= 0. Equalities are zero in both. Use bounds=[(0, None), (0, None)] with minimize; use lb=0 with fmincon.

Supply jac= if you have an analytical objective gradient. It is optional. args=(...) passes additional arguments to your objective and nonlinear constraints. Inspect help(fmincon) or help(minimize) for the full interface.

Interpreting results

• x, fun: returned point and objective.
• success: requested numerical first-order and feasibility checks passed. This is not a second-order or global-minimum certificate.
• maxcv: constraint violation in your original units.
• usable: a usable-point status; it does not replace checking success.
• message, notes: termination reason and solver diagnostics.
• nfev, nit: objective calls across the portfolio and iteration count.

Always examine the status and feasibility before using the result. An Acceptable or stagnation exit has success=False. Finite differences and noisy model evaluations limit attainable accuracy.

Current scope

Implemented: primal-dual interior point, feasibility restoration, automatic gradient scaling, bounded finite differences with retreat, Jacobian sparsity detection/coloring and a portfolio of interior-point configurations. Python callbacks run serially. SQP, sparse user Jacobians, limited-memory curvature, hard per-callback evaluation budgets and progress callbacks are not complete. maxfev and time limits are checked between batches/iterations; they cannot interrupt an ongoing callback. The derivative checker needs further validation for failed or unevaluable checks; it is not a certificate.

The local development suite passes 54/54 expected fixture outcomes, with 40 strict Optimal returns. Fixture passes also include accurate points with non-success statuses and expected infeasible/unbounded diagnostics. Broader CUTEst and matched competitor comparisons remain outstanding.

License

MIT OR Apache-2.0. Rust dependency notices are included in the installed package as THIRD_PARTY_LICENSES.txt. Source is included in the source distribution; no MATLAB installation or license is required.