EDB — 17D

[17D] Topics:projection.Difficulty:*. Note:This is the well-known ”projection theorem”, which holds for $A$ convex closed in a Hilbert space; if $A\subset {ℝ}^n$ then the proof is simpler, and it’s a useful exercise..

Given $A\subset {ℝ}^n$ closed convex non-empty and $z\in {ℝ}^n$, show that there is only one minimum point $x^{\ast }$ for the problem

(Note that this last condition is simply saying that the angle must be obtuse.)