quasiconvex function

Definition

Function $f: S \to \mathbb{R}$ defined on convex subset $S$ of real vector space is quasiconvex if for all $x,y \in S$ and $\lambda \in [0,1]$,

Notes

• For a quasiconvex function, all of the sublevel sets are convex.
• All convex functions are quasiconvex.

References

1. https://en.wikipedia.org/wiki/Quasiconvex_function
2. https://math.stackexchange.com/questions/4518389/what-is-the-difference-among-pseudoconvex-quasiconvex-and-convex-functions