A set is convex if line between two points in the set stays in the set.
A function is convex if all the points above form a convex set. That is,
- A convex function multiplied by a non-negative constant is convex
- Norms and squared norms are always convex
- The sum of convex functions is convex
- The max of convex functions is a convex function
- The composition of a convex function and linear function , is convex