I need to solve the following problem (preferably in python but any other suggestion is welcome)
$$ \min_x||Ax - b||_2 $$ $$ s.t. \: Dx = Dy $$
everything except x is known. $A$ and $D$ are square sparse matrices, $x$,$y$ and $b$ are vectors. From what I understand, without the constrain the problem is solvable using the pseudo-inverse, however I am having trouble incorporating the constrain.