I was stumble upon this paper "A sequential parametric convex approximation method with applications to non-convex truss topology design problems" by Amir Beck at:
https://web.iem.technion.ac.il/images/user-files/becka/papers/29.pdf
In this paper, a non convex constraint that is a bi linear term is upper bounded by a linear approximation. This linear approximation transform the original optimization problem into solving a sequence of easiere convex problem hence the name suggest.
I am not sure why this upper bounding would work ? And it seem to me that it is why difficult to derive an upper bounding for a general non convex constraint.
If you relax the constraints by replacing them with underestimators, you make the feasible set larger. Therefore solving the problem produces a lower bound of the original objective (you perform better, since you have looser constraints).
On the contrary, if you tighten the constraints by replacing them with overestimators, you make the feasible set smaller (as if you added some constraints to the original problem). You cannot perform better, so you produce an upper bound of the original objective (provided that this tightened problem is feasible).