I am reformulating a problem via Benders decomposition technique. It is a MIQP problem. To solve the problem to the optimality with this reformulation, I have to solve many MILP problems(master problems in Benders) iteratively to the optimality. To avoid great number of iteration, I want to add cuts to the problem while single MILP is running(without interrupting the solver). For example, finding a feasible solution and adding this cut to the CPLEX while it is solving single MILP to the optimality may decrease the total number of iterations and may help to decrease the total solution time. I understand that this can be done by using callback function. Could you correct me if I am wrong(fquestion is for the callback function, I am not asking for the technique)? If this can be done, is there anyway to do this in MATLAB environment or do I need to implement it in another environment like C++or Python?
Many thanks for your help.