osqp-solver

OSQP Solver

Scope

Work only with the continuous convex QP

[ \begin{array}{ll} \operatorname{minimize} & \frac12 x^\top P x + q^\top x \ \operatorname{subject\ to} & l \leq A x \leq u, \end{array} \qquad P=P^\top\succeq 0. ]

Treat OSQP as a numerical solver, not as a modeling oracle. Derive the model, check dimensions and convexity, solve, and then independently verify what the returned status means.

Route elsewhere when the task contains integer variables, a genuinely indefinite (P), nonlinear constraints, or cones that cannot be represented by linear bounds. Do not claim that failure to detect nonconvexity proves convexity.

Workflow

1. Freeze the interpreted model

Write a short modeling checkpoint before executable code:

source:
variables and units:
objective before conversion:
constraints before conversion:
canonical P, q, A, l, u:
dimensions and expected sparsity:
why P is positive semidefinite:
requested accuracy and runtime budget:
ambiguities:

Confirm any interpretation that changes the mathematics. Keep the factor (\tfrac12) visible: if the original quadratic is (x^\top Qx), then OSQP usually needs (P=2Q).

2. Inspect the environment

Run the non-mutating probe:

python3 scripts/check_osqp_environment.py --json

Require osqp, numpy, and scipy. If they are missing, report:

python3 -m pip install 'osqp>=1,<2'

Obtain approval before changing an existing environment. Do not infer solver availability from a package listing alone; import it with the probe. Require ready: true: an importable but unsupported OSQP major version is not ready for this runner.

3. Construct solver data deliberately

• Store P and A as scipy.sparse.csc_matrix.
• Reject materially asymmetric input. For differences within the declared symmetry tolerance, construct one canonical symmetric P and use that same matrix for the PSD, objective, stationarity, setup, and update checks. Pass its upper triangle to OSQP because the solver uses upper-triangular storage.
• Encode one row of (l\leq Ax\leq u) per equality, interval, lower bound, or upper bound. Use numpy.inf for open sides.
• Check P.shape == (n, n), q.shape == (n,), A.shape == (m, n), and l.shape == u.shape == (m,).
• Check l <= u, finite P, q, and A, and the scale of every row and column. Avoid accidental dense construction for large problems.