Excellent article! Very clear and engaging.

If checking for an intersection between two convex sets, another method is to solve a convex optimization problem minimizing the norm of the difference between two points, one constrained to be in the first (convex) set and the second constrained to be in the second (convex) set. If the optimal value is zero, then the sets have an intersection.

I'd be curious to see a comparison between the GJK algorithm and using convex optimization. Not sure if either has an advantage over the other.