i have an optimization problem in the form:

$min ||x - y||$

sbj to:

$A.x = 0$

$A.y = 0$

$l_x \leq x \leq u_x, l_y \leq y \leq u_y$

I'm trying to find the dual form of this optimization problem, kkt can be used in this case, but i'm trying to avoid the non linearity that appears in the constraints. Does the strong duality for linear programming apply to this type of problem? or there are some steps that are different and i need to keep in mind?