# floor/ceiling/round functions in the constraints of an optimization?

I have a constrained optimization problem in which I have to impose a "floor" or "ceiling" constraint to the solution. In fact I decided to use these nonlinear rounding functions because I needed to have an integer solution (or sometimes multiple of a specific scalar). My problem can be simplified as:

$D=||AX+B||_2$

minimize $D,$

s.t. $x_1=round(x_1), x_2=round(x_2), ... ,x_n=round(x_n)$

I know this notation is not perfect! I just wanted to mathematically show what I need.

So my question is that: Is there any way to have such constraints in an optimization? A "solvable!" problem of course, because I'm no expert in this field.