| name | kkt-checker |
| origin | workshop |
| description | Verify that a candidate primal-dual point (x, y, z) satisfies the KKT
conditions for a QP or NLP of the form
min f(x) s.t. A x = b, x >= 0
Reports max residuals for stationarity, primal feasibility, dual
feasibility, and complementarity. Use whenever a "candidate solution"
is reported and you want to confirm it is a KKT point, or to inspect
per-block residuals.
|
KKT checker skill
Use this skill when:
- The user reports a candidate solution
(x, y, z) from any solver and wants verification.
- The user wants residuals broken down by KKT block (stationarity, feasibility, complementarity).
- The user asks "is this a KKT point?" for a problem of the supported form.
How to invoke
python .claude/skills/kkt-checker/check_kkt.py \
--problem problem.py \
--solution solution.json \
--tol 1e-8
The --problem argument should point to a Python file exposing a get_qp() function returning (Q, c, A, b). The --solution argument should point to a JSON file with arrays x, y, z.
Output looks like:
Stationarity: max |Qx + c - A^T y - z| = 1.23e-12
Primal feas: max |A x - b| = 0.00e+00
min x_i = 1.33e-01
Dual feas: min z_i = 0.00e+00
Complement: max |x_i * z_i| = 0.00e+00
==> KKT residual = 1.23e-12 (< tol = 1.00e-08): PASS
Interpreting the output
- Stationarity failures usually indicate a wrong gradient or a missing multiplier block.
- Primal feasibility failures: the point is not on the feasible set. Check the equality constraint and bounds.
- Dual feasibility failures: a multiplier
z_i < 0. Either the solver returned the wrong sign, or your problem is being interpreted as x <= 0 instead of x >= 0.
- Complementarity failures:
x_i > tol and z_i > tol simultaneously. Check whether the active set was identified correctly.
Extending
To handle inequality constraints g(x) <= 0, add g, jac_g to the problem interface and a third multiplier block. Keep the four-residual layout — it is the cheapest way to localize what failed.
