Professor Yash Pant talked about this.
Noam Brown also talks about this.
- Course by Stanford: https://see.stanford.edu/Course/EE364A
Also heard about this from the Ericsson guy I played golf with, when he was doing his PhD.
Soham also explained this to me. But basically, it’s the idea that there exists a longest point for a given function. Having convex functions give these really nice properties which allows you to solve them more easily.
Convex Function: a real-valued function is called convex if the line segment between any two points on the graph of the function lies above the graph between the two points.
If you draw a line between any two points, the curve will be below the line.