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?