Accelerated gradient methods with absolute and relative noise in the gradient

Abstract

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