Suppose than during the execution of CPLEX, some oracle gives me valid lower bounds for the problem (minimization problem). So, I would like to give these bounds to CPLEX using cut callbacks, as objective value cuts: (say \sum_ic_ix_i is the objective function)

\sum_ic_ix_i >= LowerBound

My questions are:

- These cuts potentially cut off feasible integer solutions, which user cuts are not supposed to do. But I know they won't cut off any optimal solution. Should I add them as user cuts?
- I imagine that considering these cuts as lazy cuts won't help me much in terms of improving the LP relaxations, so adding them as lazy cuts would be a bad idea, right?

Any feedback is welcome.

Thanks!