  Existing asynchronous distributed optimization algorithms often use
diminishing step-sizes that cause slow practical convergence, or fixed
step-sizes that depend on an assumed upper bound of delays. Not only is such a
delay bound hard to obtain in advance, but it is also large and therefore
results in unnecessarily slow convergence. This paper develops asynchronous
versions of two distributed algorithms, DGD and DGD-ATC, for solving consensus
optimization problems over undirected networks. In contrast to alternatives,
our algorithms can converge to the fixed-point set of their synchronous
counterparts using step-sizes that are independent of the delays. We establish
convergence guarantees under both partial and total asynchrony. The practical
performance of our algorithms is demonstrated by numerical experiments.
