| # Projection on a polyhedron Recall that a polyhedron is an intersection of a finite number of half-spaces. A polyhedron can be written as where and , and the symbol refers to the component-wise inequality between vectors. The Euclidean projection (or projection for short) of the origin on the polyhedron is the (unique) solution to the optimization problem Without loss of generality, we can square the objective and solve the problem The above is a QP.