In my optimization problem the objective function and all the constraints are linear. The decision variables are binary. [so, it's BLP] Some of the hard constraints are very time-consuming to be solved, therefore I would like to relax them by the lagrangian multipliers (ie, putting them into the objective function in a penalized way). The optimization software I'm using (lpSolve) provides the dual solution of the simplex method (it retrieves the values of the dual variables (the reduced costs)). BUT I don't know what's the relationship btw the dual solutions and the relaxed constraints to be put in the objective function.