In many cases you can actually insert outside numbers in the middle of the solver process via callbacks. For example see IncumbentUpdater at https://python-mip.

In many cases you can actually insert outside numbers in the middle of the solver process via callbacks. For example see IncumbentUpdater at https://python-mip.readthedocs.io/en/latest/classes.html https://python-mip.readthedocs.io/en/latest/classes.html And various C APIs for solvers have other callbacks It's generally quite limited of course, for the reasons you mentioned.