We are solving How to get intersection point(s) of two glyphs? and if we could find minimum distance between two Bézier curves analytically, it would be computationally effective. It would be much better method than bisection method we quite often use in typography.
A mathematician told me that this approach could lead into a horrible system of equations. That's likely reason we use numerical methods instead.
One of my (poor) ideas is to convert Bézier curves to spiral curves (see application in FontForge), but it might lead us into an even worse situation (from mathematical point of view).
My next idea is to split up Bézier curves into smaller parts, but it's probably not improving a thing. I'm sorry I'm not providing MWE, please feel free to delete/close my question.