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.
Newton-type methods for optimization and variational problems
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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.