Cutting plane methods can be extended into nonconvex optimization [article]

Oliver Hinder
2019 arXiv   pre-print
We show that it is possible to obtain an O(ϵ^-4/3) expected runtime — including computational cost — for finding ϵ-stationary points of smooth nonconvex functions using cutting plane methods. This improves on the best-known epsilon dependence achieved by cubic regularized Newton of O(ϵ^-3/2) as proved by Nesterov and Polyak (2006). Our techniques utilize the convex until proven guilty principle proposed by Carmon, Duchi, Hinder, and Sidford (2017).
arXiv:1805.08370v4 fatcat:p7sfjapwfvh6xeormg3kztryny