Let's say we are using Integer Programming in order to minimize an objective function. We are interested in computing a lower bound for the problem.
My question is: when should we use a Linear Programming relaxation, and when should we use a Lagrangian relaxation? Is there some intuition in when one relaxation would be better than the other? In particular, consider the situation in which there are no specific "complicating" constraints in the problem (e.g. all the constraints seem equally important).