Stopping Rules for Gradient Methods for Non-convex Problems with Additive Noise in Gradient

We study the gradient method under assumption that an additively inexact is available for, generally speaking, non-convex problems. The non-convexity of objective function, as well use inexactness specified at iterations, can lead to various For example, trajectory may be far enough away from starting point. On other hand, unbounded removal in presence noise desired global solution. results investigating behavior are obtained and condition dominance. It known such a valid for many important Moreover, it leads good complexity guarantees method. A rule early stopping proposed. Firstly, achieving acceptable quality exit point terms function. Secondly, ensures fairly moderate distance this chosen initial position. In addition with constant step, its variant adaptive step size also investigated detail, which makes possible apply developed technique case unknown Lipschitz gradient. Some computational experiments have been carried out demonstrate effectiveness proposed methods.