Fast projection onto the simplex and the ball

A new algorithm is proposed to project, exactly and in finite time, a vector of arbitrary size onto a simplex or an -norm ball. It can be viewed as a Gauss-Seidel-like variant of Michelot's variable fixing algorithm; that is, the threshold used to fix the variables is updated after each element is read, instead of waiting for a full reading pass over the list of non-fixed elements. This algorithm is empirically demonstrated to be faster than existing methods.