how to obtain the solution information of subproblem when using callback
Dear all,
Currently, I am trying to implement a Benders Decomposition. I can add a lazy constraint to limint the binary variables of the master problem. I can obtain the optimal solution of the master problem after many iterations.
Actually I can obtain more information from the subproblem. I know the solution value of the subproblem actually gives a upper bound UB for the objective function Z of the master problem. I try to reduce the maximum possible value of Z by using the constraint Z<=UBepsilon where epsilon is a very small value, such as epsilon =1. When adding the constraint, the master problem reports infeasible very soon. I want to know how to add the solution value of the subproblem to limit the objective function of the master problem.
Thanks very much

Hi,
Are you sure that subtracting \(\epsilon=1\) from your upper bound is valid? E.g., the optimal objective value of your master problem is \(Z=2\) and the upper bound you get from one of your subproblems is \(UB=2.5\). Then, adding the constraint \(Z\leq UB\epsilon\) may make your master problem infeasible. Is there a particular reason why you subtract the \(\epsilon\)? What happens if you don't subtract the \(\epsilon\) but still add the constraint \(Z\leq UB\)?Best regards,
Jaromił 
Hi,
You are right. But I am trying to tighten the upper bound for speeding up the solution process. If the UB=10 and \(\epsilon=1\), \(Z=9\) for next iteration by using \(Z\leq UB\epsilon\). But there is a risk to cause the model infeasible. Do you have any good suggestion? If I just add \(Z\le UB\), it is slow to help the model to find a good upper bound sometimes.

Hi,
We recently added a knowledge base article, which could provide some insight on your problem.
Best regards,
Jaromił
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