solve the question

3.1.12 (Projection on a Simplex) (a) Develop an algorithm to find the projection of a vector z on a simplex. This algorithm should be almost as simple as a closed form solution. (b) Modify the algorithm of part (a) so that it finds the minimum of the cost function n S(x) = (orit Bir?) over a simplex, where o and B; are given scalars with 3; 0. Consider also the case where B, may be zero for some indices