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In this paper, we investigate accelerated first-order methods for smoothconvex optimization problems under inexact information on the gradient of theobjective. The noise in the gradient is considered to be additive with twopossibilities: absolute noise bounded by a constant, and relative noiseproportional to the norm of the gradient. We investigate the accumulation ofthe errors in the convex and strongly convex settings with the main differencewith most of the previous works being that the feasible set can be unbounded.The key to the latter is to prove a bound on the trajectory of the algorithm.We also give a stopping criterion for the algorithm and consider extensions tothe cases of stochastic optimization and composite nonsmooth problems.

Accelerated gradient methods with absolute and relative noise in the gradient