Computationally compare 2 lagrange relaxations

The point is to compare two different Lagrangean relaxations for a UFLP that I will provide. This also involves the design/adaptation of a simple heuristic algorithm to compute upper bounds at some iterations of the LR.

The objective is to to compare the performance of the subgradient algorithm that is used to solve the Lagrangean dual problems. Different values of the parameters have a significant performance in the convergence of this algorithm. Investigate what configuration of parameters would lead to the best performance in practice (in terms of %gap and CPU time) for both considered relaxations. You are responsible of designing the computational experiments that may be needed to achieve your objective.

You have to summarize the findings in a report. It must contain a clear description of the two relaxations (e.i., the formal definition of the Lagrangean function and the Lagrangean Dual Problem, the algorithms used to evaluate L(\lambda), etc) and a summary of the results obtained from your computational experiments.

I will be providing a code on C and Cplex to help with this task.