I'm solving a mixed-integer problem via branch and cut using both a Lazy Constraint callback (where I add the violated constraints) and a User Cut callback to implement other cuts. I would like to check if there are violated constraints at each node of the branching tree and not only when I find an integer feasible solution, so I added the procedure to check the constraints also in the User Cut callback. But I'm wondering if Cplex always adds the violated inequalities or if it only adds the ones that don't cut off integer-feasible solutions, as I'm inside a User Cut callback. If this is the case, is there a way to add violated constraints at each node? (I'm using Cplex 12.4 with Python)
Thank you very much for your help!