auto_math_constraints_duality_and_shadow_prices_2

Snippet from Math-Constraints-Duality-and-Shadow-Prices.md

def check_constraint_qualification(A: np.ndarray, x: np.ndarray, b: np.ndarray) -> dict:
    """Verify qualifications at x."""
    slack = b - A @ x
    active = np.where(slack < 1e-6)[0]
    
    if len(active) == 0:
        return {"qualified": True, "reason": "interior"}
    
    A_active = A[active]
    rank = np.linalg.matrix_rank(A_active)
    
    qualified = (rank == len(active))
    
    return {
        "qualified": qualified,
        "active": active.tolist(),
        "rank": int(rank),
        "expected": len(active),
        "reason": "LICQ" if qualified else "violated"
    }