I am not sure if this is the right place to post this question, please point me to the correct forum if I posted in a wrong place.

I have an optimization problem like this

```
Min sum(yi)
st sum on j(wij) <= cyi for all i in N
sum on i(xij) = 1 for all j in N
wij = wjxij for all i, j in N
Lij = Ljxij for all i, j in N
Dij = Lij + wij for all i, j in N
(Lij - Dik)(Lik - Dij) <= 0 for all i, j, k in N
Aj <= Lj for all j in N
Lj <= Aj + Qj for all j in N
xij = 0 or 1 for all i, j in N
yi = 0 or 1 for all i in N
Wj, Lj, Qj and c are constant
N = 10000
```

What can I do to transform this problem into a convex optimization problem? Or to a linear Integer programming problem? Because I only know algorithms to solve problems in those two categories.

In the problem, the only constraint that is not convex is this one

```
(Lij - Dik)(Lik - Dij) <= 0 for all i, j, k in N
```

Are there any common ways to transform this constraint into some convex constraints?

I think implicit enumeration could be a solution to this, but other than that, what can i do?