Proximal point algorithm achieves O(ε^{-1}) complexity for quasar-convex functions and linear convergence with O(ln(ε^{-1})) for strongly quasar-convex functions.
Polyak , Existence theorems and convergence of minimizing se- quences in extremum problems with restrictions, Soviet Math
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Extending Linear Convergence of the Proximal Point Algorithm: The Quasar-Convex Case
Proximal point algorithm achieves O(ε^{-1}) complexity for quasar-convex functions and linear convergence with O(ln(ε^{-1})) for strongly quasar-convex functions.