I wrote a couple of miscellaneous posts on polyhedron-related stuff for my game physics series on my blog.
The first post explains how you can use the half edge data structure to implement a better support function for polyhedrons utilizing a hill-climbing approach, as opposed to the most obvious brute-force approach. It also shows an example implementation of dynamic half edge data structure.
The second post demonstrates 3 options for updating the AABBs of polyhedrons, namely the brute-force approach, approximation by local AABB, and the support function approach. This posts also touches on their pros and cons.
Here's a list of all posts of the game physics series that lead up to these two posts.
I hope you like it