Active Set

The active set $\mathcal{A}(x)$ at any feasible $x$ consists of the equality constraints indices from $\mathcal{E}$ together with the indices of the inequality constraint $i$ for which $c_i(x)=0$; that is,

$$\mathcal{A}(x)=\mathcal{E}\cup \{i\in \mathcal{I}|c_i(x)=0\}$$

At a feasible point $x$, the inequality constrain $i\in \mathcal{I}$ is said to be active if $c_i(x)=0$ and inactive if the strict inequality $c_i(x)>0$ is satisfied.

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