  We study the convergence of Nesterov Accelerated Gradient (NAG) minimization
algorithm applied to a class of non convex functions called strongly quasar
convex functions, which can exhibit highly non convex behaviour. We show that
in the case of strongly quasar convex functions, NAG can achieve an accelerated
convergence speed at the cost of a lower curvature assumption. We provide a
continuous analysis through high resolution ODEs, in which negative friction
may appear. Finally, we investigate connections with a weaker class of non
convex functions (smooth Polyak-\L ojasiewicz functions) by characterizing the
gap between this class and the one of smooth strongly quasar convex functions.
