I am trying to find the optimal integer solution of a IP by solving a sequence of LPs instead of MILPs. What I am currently doing is I resolve the entire LP from sketch after adding some certain cuts. LP can be solved relatively efficient via Simplex, but my LP model might be extremely large after several iterations after adding cuts.
Even though I can get my expected solution in this way, I am wondering if there is more efficient way in Gurobi to solve the problem after adding cuts (maybe use some certain Callback functions such that Gurobi does not need to use all constraints in the model?).
Given a MIP, my expected procedure is: solve its continuous relaxation (RP) --> add cuts to (RP) if needed and ignore nonlinear constraints, so that the new problem is a (LP) --> solve the new continuous problem(LP) --> add cuts to (LP) if needed-->...--> until get the integer solution.
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