Stopping rules for accelerated gradient methods with additive noise in gradient

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.

Keywords

Accelerated methods, inexact gradient, stopping rule, inverse problems

URI

https://oa.tib.eu/renate/handle/123456789/9530
https://doi.org/10.34657/8568

Citation

Vasin, A., Gasnikov, A., & Spokoiny, V. (2021). Stopping rules for accelerated gradient methods with additive noise in gradient (Vol. 2812). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik. https://doi.org//10.20347/WIAS.PREPRINT.2812

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Mathematik

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