  We analyze a class of exact distributed first order methods under a general
setting on the underlying network and step-sizes. In more detail, we allow
simultaneously for time-varying uncoordinated stepsizes and time-varying
directed weight-balanced networks, jointly connected over bounded intervals.
The analyzed class of methods subsumes several existing algorithms like the
unified Extra and unified DIGing (Jakovetic, 2019), or the exact spectral
gradient method (Jakovetic, Krejic, Krklec Jerinkic, 2019) that have been
analyzed before under more restrictive assumptions. Under the assumed setting,
we establish R-linear convergence of the methods and present several
implications that our results have on the literature. Most notably, we show
that the unification strategy in (Jakovetic, 2019) and the spectral step-size
selection strategy in (Jakovetic, Krejic, Krklec Jerinkic, 2019) exhibit a high
degree of robustness to uncoordinated time-varying step sizes and to
time-varying networks.
