We are given a matrix $A$ and vectors $b,d$ of appropriate size and we want to solve
$$\begin{cases}\min_x ||Ax-b||_2 \\ \text{s.t.}\\ 0\leq x\leq 2d\end{cases}$$ where the inequality has to be understood componentwise.
Does anyone know how to solve this problem? Does there exist an explicit solution? Without the constraint $0 \leq x \leq 2d$ this is the linear least-square problem. Of course we could take the inequality in as a penalty contraint, but maybe there already exist more sophisticated possibilities, that I am not aware of?
There are several methods to solve this kind of problem. See for example this and this.