Is it possible to get the value of the Interior Solution ?
OngoingHello,
I would speed up my model which works with Bender's decomposition. For this I will use the Pareot Optimal Cuts. These require a socalled Core Point, Analytic Center or Interior Solution (which should be the same).
I have read that Gurobi MILP can solve with Simplex or Barrier. The Barrier method is nothing different than an Interior Solver.
In the Barrier method the result of the Interior is converted into the Basic Solution in the last step by crossover.
But I would like the Interior Solution and I have no idea how to get it ?
My idea was to set the solver to Barrier and disable crossover.
But I don't think that the result I get is the Interior Point.
Best Regards
Max

Hi Paul,
The Barrier algorithm without crossover, i.e., Crossover set to 0, in general returns a solution positioned in the analytic center of the optimal facet (or at least very close to it). This should be the the interior point you are looking for.
Note that this applies to LPs. For MIPs, Barrier (if set) is used to solve the LP relaxations.
Please also note that the analytic center and an interior solution do not necessarily mean the same. In general, an analytic center solution is the solution in the weighted center of the optimal facet of an LP while an interior solution can be any point on this optimal facet. However, in some disciplines this small difference is omitted.
Best regards,
Jaromił0 
Good day Jaromił,
thank you for your feedback on my question.
I wanted to use the Barrier Method for a MILP, could this lead to problems ?Have you ever had any experience using Pareto Optimal Cuts for Benders decomposition ?
Best regards,
Paul Maximilian Röhrig0 
Hi Paul,
Using Barrier for a MILP will not lead to problems but you most likely will see a performance loss, since in contrast to the Simplex algorithms, Barrier cannot be warm started.
Sorry, I don't have any experience with Pareto Cuts for Benders decomposition but maybe some other Community member has and is willing to share their experience.
Best regards,
Jaromił0
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