A quasiconvex function is a function whose sublevel sets are convex. A function which is quasiconvex under every (possibly large) linear perturbation is, by definition, a convex function. In this well-written paper, motivated by applications in partial differential equations and optimal control, the authors study functions which are robustly quasiconvex, i.e., that they remain quasiconvex under small linear perturbations.