= Critical cone
The critical cone consists of linearized feasible directions along which the <objective function> has zero first-order change. For constraints $c_i\geq0$, its directions satisfy $Dc_i\,d\geq0$ at active constraints and $\nabla f^Td=0$; equality constraints impose zero linearized residual. Under the usual regularity conditions, second-order <Karush-Kuhn-Tucker conditions> test the <optimization Lagrangian> <Hessian matrix> on this cone. Positive active multipliers force their corresponding directional residuals to vanish.
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