Originally posted by: jacobmays

I'm using subgradients from a MIP as cuts in a multi-stage model. While the linear relaxation is fine, I'm curious if there is a lazy way to make these cuts stronger. What I would like to do is set up the MIP, allow CPLEX to spend a given amount of time generating valid inequalities, and return the value and dual of the optimal solution to this tighter relaxation. I'm aware I can set nodes=0 to prevent any branching, but my understanding is that CPLEX would apply heuristics and return the best available integer solution instead of what I am looking for.

Is this possible? Thanks in advance for your ideas.

Yes, you can do this using a solve callback. That callback is invoked whenever CPLEX needs to solve an LP relaxation. You can solve the LP just the standard way but then pick up the dual values etc.

Additionally you can disable heuristics (CPX_PARAM_HEURFREQ=-1) and other stuff (probing?) you don't want CPLEX to apply.