Question

Definition: Given any non-empty closed convex set C and an arbitrary vector x in R^j, there is a unique member Pcx of C closest, in the sense of the two norm, to x. The vector Pcx is called the orthogonal projection of x onto C and the operator Pc the orthogonal projection onto C.

Question: Given a point s in a convex set C, where are the points x for which s = Pcx?

Answer 1

In this case the vector and its orthogonal projection onto C coincide.