The Set of Linearized Feasible Directions

Given a feasible point $x$ and The Active Constraint Set, $\mathcal{A}(x)$, the set of linearized feasible directions is given by

$$\mathcal{F}(x)=\{\begin{array}{l}d|\{\begin{array}{ll}{d}^T\nabla c_i(x)=0& \forall i\in \mathcal{E}\\ d^T\nabla c_i(x)\ge 0,& \forall i\in \mathcal{A}(x)\cap \mathcal{I}\end{array}\end{array}$$

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