## Refining asymptotic complexity bounds for nonconvex optimization methods, including why steepest descent is o(eps^{-2}) rather than O(eps^{-2})

\(\) We revisit the standard “telescoping sum” argument ubiquitous in the final steps of analyzing evaluation complexity of algorithms for smooth nonconvex optimization, and obtain a refined formulation of the resulting bound as a function of the requested accuracy eps. While bounds obtained using the standard argument typically are of the form \(O(\epsilon^{-\alpha})\) for some … Read more