Variational characterization of convex projection
= Variational characterization of convex projection
For $p\in C$,
$$
p=\Pi_C(x)
\quad\Longleftrightarrow\quad
\langle x-p,z-p\rangle\leq0
\quad\text{for every }z\in C.
$$
= Variational characterization of convex projection
For $p\in C$,
$$
p=\Pi_C(x)
\quad\Longleftrightarrow\quad
\langle x-p,z-p\rangle\leq0
\quad\text{for every }z\in C.
$$