Moore–Penrose inverse for constrained least squares

I would like to use the generalized Moore–Penrose inverse for solving a constrained least squares problem. More explicitly, I need to find the matrix A minimizing ||AX-B||, where matrices X and B are given. The problem is that components of matrices X and B are in [0,1] while components of A must be in [-1,1]. Any idea how to deal with this problem?

• I realize the pseudoinverse solves least squares problems, but what makes you think it can be used to solve constrained least squares problems? I haven't seen that before, although it would be interesting if it turns out to be true. – littleO Oct 11 '17 at 20:11
• Do you mean that the components of $X$ (rather than $A$) are constrained to belong to $[-1,1]$? – littleO Oct 11 '17 at 20:12
• I have no reason to think that it can be possible and perhaps I am forcing the use of the pseudo-inverse to solve that problem. – Gonzalo Nápoles Oct 11 '17 at 20:16
• X and B are always in [0,1] and they are my inputs, so I must be able to find a matrix A in [-1,1] minimizing the expression above. – Gonzalo Nápoles Oct 11 '17 at 20:18
• Oh, I see. It's unusual notation to have $X$ be given and have $A$ be the unknown. Most people would expect the opposite. – littleO Oct 11 '17 at 20:19