Project to nearest point on convex polyhedron

I have a point $y in mathbb{R}^d$ and a convex polyhedron $mathcal{P}$ given as the intersection of half-spaces:

$$mathcal{P} = {x in mathbb{R}^d mid a_1 cdot x le b_1, dots, a_n cdot x le b_n}.$$

I would like to project $y$ onto the polyhedron, i.e., to find the nearest point $z in mathcal{P}$: in other words, to minimize $|y-z|_2$ subject to $z in mathcal{P}$. I know there are algorithms using quadratic programming, but I am hoping for a simple to implement method, even if it is not optimal.

Here is one possible incremental method: pick the halfspace that $y$ is furthest from, i.e., find the index $i$ that maximizes $a_i cdot y – b_i$, then project $y$ onto that halfspace, i.e., replace $y$ with $y’ = y – (a_i cdot y – b_i) a_i$, and repeat. (I have assumed, without loss of generality, the inequalities have been normalized so $|a_i|_2=1$.) While this might not yield the optimal solution, I hope that after it a fixed number of iterations it will get close to the optimal solution.

Is this a good method? Is there a better method that is simple to implement and does reasonably well?