= Linear independence constraint qualification
= LICQ
{c}
{synonym}
For smooth equality constraints $h_j=0$ and inequality constraints $g_i\geq0$, this condition requires linear independence of all equality gradients and active inequality gradients at the feasible point. It ensures existence of <Lagrange multipliers> at a local optimum and uniqueness of their values for a fixed objective gradient. It implies the <Mangasarian–Fromovitz constraint qualification> by solving the independent gradient equations with zero equality derivatives and positive active inequality derivatives.
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