I have a linear equation with 3 variables and few linear constraints. How do I find Integer values for x, y and z such that the result is as close as possible to 0 (if exactly 0 is not possible)
-2x + 3y -5z = 0
given,
1 <= x <= 20
1 <= y <= 45
1 <= z <= 45
How do I convert this problem to Integer optimization problem? Is integer optimization even required?
Let $d$ be a nonnegative (continuous) variable. Minimize $d$ subject to $$-2x + 3y -5z \le d$$ and $$-d \le -2x + 3y -5z$$plus your domain constraints for the integer variables. The optimal value of $d$ will be the absolute value of your sum.