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<math>P_Cx \in C</math> such that <math>D_C(x) = \| x - P_Cx \|_2 </math>.
The [[subdifferential]] of <math>f</math> at <math>x</math> is given by
: <math>
\partial f(x) = \{ u \in \mathbb{R}^N \mid \forall y \in \mathbb{R}^N, (y-x)^\mathrm{T}u+f(x) \leq f(y).\}
</math>
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