Using the KKT optimality condition find the orthogonal projection of an arbitrary point $c \in$ to the closed convex set $C$ (non empty) defined by:
(a) $C=\{x \in R^n : Ax\leq a\}$ where $A\in R^{mxn}$ (surjective) and $a\in R^m$.
(b) For $n=3$, $C=\{x\in R^n:<Ax,x>\leq1\}$ where $A\in R^{3x3}$ is symetric positive defined.
A hint would be appreciated, thanks in advance