Mangasarian–Fromovitz constraint qualification

At a feasible point for smooth $h=0$, $g\ge 0$, the equality gradients must be independent and there must be a direction $v$ with $Dhv=0$ and $D{g}_{i}v>0$ for every active inequality. It supplies a first-order direction strictly into all active inequality constraints while respecting the equality tangent space. This constraint qualification ensures the usual Karush-Kuhn-Tucker conditions are necessary for local optimality. For a strictly convex quadratic inequality restricted to an affine equality space, it holds at every feasible point exactly when a strictly feasible point exists; moving from a boundary point toward a strictly feasible point supplies the required direction.