I have a constraint $X \ge Y$ in a Linear programming formulation, where both $X$ and $Y$ are binary. I want to check this constraint on a condition like:
if (Y==1)
then check the constraint
else
Don't care about the constraint
How to do it.
If $X$ and $Y$ are zero-or-one (binary) integer variables, then this is encoded as
$$X \ge Y.$$
Why does this work? If $Y=1$, then this enforces the constraint $X \ge Y$, as you wanted. If $Y=0$, this enforces the constraint $X \ge 0$, i.e., it doesn't impose any rstrictions on $X$, which is also as you wanted.
In general, conditional constraints can be handled using the techniques found on page 7 of AIMMS Modeling Guide - Integer Programming Tricks, which is a helpful tutorial on how to encode constraints in integer programming. Thanks to @adrianN for pointing to that resource.
You can also take a look at https://cs.stackexchange.com/a/12118/755 and at Formulating Integer Linear Programs: A Rogues' Gallery for other techniques and practice problems.
