Stopping rules for accelerated gradient methods with additive noise in gradient

In this article, we consider an accelerated first-order method, namely, the method of similar triangles, which is optimal in the class of convex (strongly convex) problems with a gradient. The paper considers a model of additive noise in a gradient and a Euclidean prox-structure. Convergence estimates are obtained in the case of strong convexity and its absence, and a stopping criterion is proposed for not strongly convex problems.