I need to compute the nearest point of $x$ from a probability simplex. Formally, I want to ask if there is a close form for the solution to the following optimization problem: for $y\in \mathbb{R}^k$,
$$\min\limits_{x} \|x-y\|^2_2 $$
$$s.t. \ \sum\limits_{i=1}^k x_i =1,\ x_i \geq 0 ,\ \forall i \in[k]$$
If not, how can I derive an iterative algorithm to find the unique solution? Thanks!