sqp-craft

Sequential quadratic programming (SQP) for smooth constrained nonlinear problems, with a native Rust solver: damped BFGS updates of a dense Hessian approximation, step QPs solved by Clarabel (interior point, the default) or a dense active-set backend, and an ℓ1 merit line search. Results report stationarity, complementarity and dual-sign residuals of the KKT conditions, and kkt_residuals and check_derivatives check points and derivatives independently.

Install

python -m pip install sqp-craft

Wheels (abi3, CPython 3.10 or newer) cover Linux x86_64, Windows x64 and macOS x86_64/arm64 and need no compiler. On other platforms pip builds the source distribution, which needs Rust 1.85 or newer. The package depends on nothing else at run time.

Example

from sqp_craft import ProblemSpec, check_derivatives, solve

class Model:
    """minimize (x0-2)^2 + (x1-1)^2  subject to  x0^2 - x1 <= 0,  x0 + x1 <= 2"""
    def functions(self, x):
        return (x[0] - 2) ** 2 + (x[1] - 1) ** 2, [x[0] ** 2 - x[1], x[0] + x[1]]

    def derivatives(self, x):  # gradient, then the Jacobian values in CSR order
        return [2 * (x[0] - 2), 2 * (x[1] - 1)], [2 * x[0], -1.0, 1.0, 1.0]

inf = float("inf")
spec = ProblemSpec(lower=[-5, -5], upper=[5, 5],
                   constraint_lower=[-inf, -inf], constraint_upper=[0, 2],
                   jacobian_indptr=[0, 2, 4], jacobian_indices=[0, 1, 0, 1])
assert check_derivatives(spec, Model(), [0.5, 0.5]).passed
result = solve(spec, Model(), [0.5, 0.5], method="sqp")
print(result.status, result.candidate, result.evaluation.objective)
# converged, candidate ≈ [1, 1], objective ≈ 1

Pass method="sqp": the default method="dummy" only evaluates the start point. SqpOptions configures the solver (iteration, callback and time limits, KKT tolerances, qp_solver="clarabel" or "active-set", elastic_mode with the active-set backend for infeasible linearizations); invalid values raise ValueError. Callbacks run serially on the calling thread.

Limits

• Smooth (twice continuously differentiable) objective and constraints with first derivatives; kinks, noise and branches break BFGS and the line search.
• At most 256 variables (dense BFGS). For larger sparse problems, an IPOPT-family solver fits better.
• A local method: converged means a first-order KKT point within the tolerances, not a global optimum. Use several starts for multimodal models.

More

• Repository, with the multistart examples and the source build; the Rust crates start at sqp-craft-solver
• AI agent guide: modelling, options, results, multistart and the job API
• Changelog
• Shared solver-selection guide and ecosystem overview: when black-box optimization (fcmaes) or LP/MIP (LP-IP-craft) fits better, and durable shell/MCP jobs through the sqp-job-worker (built from source)

MIT license.