Moore–Penrose inverse for constrained least squares

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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?