  In this paper, we investigate accelerated first-order methods for smooth
convex optimization problems under inexact information on the gradient of the
objective. The noise in the gradient is considered to be additive with two
possibilities: absolute noise bounded by a constant, and relative noise
proportional to the norm of the gradient. We investigate the accumulation of
the errors in the convex and strongly convex settings with the main difference
with 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 to
the cases of stochastic optimization and composite nonsmooth problems.
