nomenclature question: nonconvex functions with only saddle points and global minima

Question

Is there a categorical term used to describe all nonconvex functions whose critical points are only saddle points and global minima? I am working on a nonlinear structured matrix factorization problem with these properties and would like to learn more about the general properties of such functions. From what I understand, any quasiconvex function would fall under this description but not all functions with these properties are quasiconvex since $f(\lambda x + (1-\lambda)y) \leq \max \{f(x),f(y)\}$ for $\lambda \in [0,1]$ is not necessarily true.

Answer 1

Since a critical point is either a local minimum, a local maximum or a saddle point, these are just the functions with no local maximum and no non-global local minima. Any differentiable function falls into this class if you restrict the domain to exclude any local maxima and non-global local minima. So I doubt that you'll get very much in the way of properties.