I am implementing Benders Decomposition via callbacks. Subproblem can only be solved by Barrier algorithm (simplex and dual simplex are incompetent). When there is a solution for the subproblem, the Barrier can solve it in 15 seconds and the optimality cuts could be added successfully. However, when the subproblem is unbounded, the Barrier barely finishes the ordering the matrix (in hundreds of seconds) and consumes lots of memory (over 200 GB). Gurobi suggests tuning different parameters (BarOrder, BarHomogeneous etc.) to deal with unboundedness. But changing them other than default parameter is worsening the solution of feasible subproblem (the algorithm can not even finish ordering the matrix).
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