I am applying Lagrangian Relaxation with Subgradient Optimization Method and trying to solve a MIP model. Before testing the large-scale instances, I wanted to see how it performs on small-size ones. I have a great problem which makes me desperate for days and I need the ideas of experienced people in OR Community of SE. I know that in SO method, choosing the good values for the parameters is highly important. Even if I apply many trial and fail tests , I get the same result: The lower bound converges well until a certain point and when the best lower bound is found as 0, (the optimum value is 1) it is getting stuck there. After that moment in the following iterations, the newly found lower bounds change slightly such as from -3,9677 to -3,8599 , so best lower bound is kept as 0. It never goes beyond 0 towards to optimum value which is 1. I got stuck at this point and I do not know which path should I follow now. I checked the evolution of multipliers etc, they all correct.
If anyone who experienced the same issue or has knowledge about this case, shares ideas with me, I will be very happy , what should I do know?
Thank you so much