I understand that quasiconvex functions are defined as having convex lower level sets. Unimodal functions are defined as those where the function is non-decreasing in every direction away from the minimum. Hence, quasiconvex functions are always unimodal, at least for the continuous ones.
My question is:
From a practical point of view; as in an iterative solver trying to find the minimum, is there any significance of quasiconvex functions over simply unimodal but not quasiconvex ones? Is either of them easier to prove than the other?