Constraint Qualification

An assumption that ensures similarity of the constraint set $\Omega$ and its linearized approximation in a neighborhood of a point $x^{\ast }$.

Also ensures that the linearized feasible set $\mathcal{F}(x^{\ast })$ and the tangent cone $T_{\Omega }(x^{\ast })$ are the same.

Why is it needed: fact check this They are needed to rule out special cases where optimal solutions does not fulfill the KKT (Karush–Kuhn–Tucker) Conditions.

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