A randomized algorithm for nonconvex minimization with inexact evaluations and complexity guarantees

arXiv:2310.18841v2 Announce Type: replace-cross
Abstract: We consider minimization of a smooth nonconvex function with inexact oracle access to gradient and Hessian (without assuming access to the function value) to achieve approximate second-order optimality. A novel feature of our method is that if an approximate direction of negative curvature is chosen as the step, we choose its sense to be positive or negative with equal probability. We allow gradients to be inexact in a relative sense and relax the coupling between …

abstract algorithm arxiv complexity cs.lg feature function gradient math.oc negative novel oracle type value