Answer to Question #36205 in Math for Matthew Lind

Question

Proposition: Given any nonempty 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 (or metric) 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?