| # Projection of a convex set on a subspace The projection of a point on a set is the point that is closest (in the sense of Euclidean norm) to the set. Mathematically the projection of a point on a convex set is the (unique) solution to the optimization problem The projection of a whole set on another set is simply the set of projections , when runs . The projection of a convex set on any subspace or affine set is convex.
| The image shows the convex set and its projection on the space of variables. The projection turns out to be the set Since the original set is convex, its projection also is.