Suppose $x_1, x_2, \ldots, x_n$ each take values zero or one and we want to solve the following linear programming problem:
$$ \min_{x_1,x_2,\ldots, x_n} f(x_1,x_2,\ldots,x_n) $$ subject to a bunch of constraints. Suppose $f$ is linear.
Can I have one of those constraints be $x_1+x_2 \ne 1$ (or alternatively $x_1+x_2=0$ OR $x_1+x_2=2$)?
It's still a well-defined problem with a constraint like that, but can we use standard algorithms to solve it? In some sense, it seems conceptually pretty easy. My hope is that this is a pretty standard problem and one that can be easily worked with in Gurobi or CPLEX, but I've never had to work with a constraint like this before.