# Projection onto Polyeder

I know how to projects onto a linear subspace of $\mathbb R^3$, but how to project a point $x$ onto an polyhedron given as the intersection of three halfspaces $$\langle y_1, x \rangle \ge c_1 \mbox{ and } \langle y_2, x \rangle \ge c_2 \mbox{ and } \langle y_3, x \rangle \ge c_3?$$

$$min_z ||x-z||_2$$
$$\langle y_i^T z\rangle \geq c_i , i=1,\ldots$$