WIAS Preprint No. 2812, (2021)

Stopping rules for accelerated gradient methods with additive noise in gradient


  • Vasin, Artem
  • Gasnikov, Alexander
    ORCID: 0000-0003-1201-2343
  • Spokoiny, Vladimir
    ORCID: 0000-0002-2040-3427

2020 Mathematics Subject Classification

  • 90C30 90C25 68Q25


  • Accelerated methods, inexact gradient, stopping rule, inverse problems




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.

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