Originally posted by: violets

I have an integer programming not only with large number of variables but also large number of constraints. For example, more than 10^7 variables, more and more constraints. And, CPLEX can't solve this model. The main reason is that some kinds of constraints are considered to describe the relationship among variables. Factually, two constraints for each variable in my case.

As far as I know, Lagrangian relaxation and column generation could effectively deal with JUST large number of variables. Additionally, my formulation could not be decomposed into sub-problems because of cross relationship constraints. My question is how to do an integer programming with this situation?

Thanks!

What exactly does "can't solve" mean? Does it fail to even build the model in memory? Does it not find feasible solutions? Does it not manage to prove optimality? Can you attach an instance of your model here?

Would it be an option to separate some of your constraints as lazy constraints?