I am trying to decompose my MINLP problem in master (integer problem) and subproblem (nonlinear). It is a Power System optimization problem. I do not have a specific example in mind, but after doing much reading I am still stuck at the following questions.
Is Benders method different when the subproblem is nonlinear compared when it is linear?
In order to decide the optimality/feasibility cuts, how dual variables are selected? In some literature, the dual variables are used from each constraint (with and without binary variables) in subproblem; however, in others, the dual variables are only selected from the constraint with binary variables. Even in some more, new variables are assigned to binary decision variables (equality), and the dual variable only from these equalities are used.
If there are conditional (if/else) constraints in the subproblem, do the integer variables from these constraints require any special treatment? Can subproblem still be treated as NLP?