  We present complexity and numerical results for a new asynchronous parallel
algorithmic method for the minimization of the sum of a smooth nonconvex
function and a convex nonsmooth regularizer, subject to both convex and
nonconvex constraints. The proposed method hinges on successive convex
approximation techniques and a novel probabilistic model that captures key
elements of modern computational architectures and asynchronous implementations
in a more faithful way than state-of-the-art models. In the companion paper we
provided a detailed description on the probabilistic model and gave convergence
results for a diminishing stepsize version of our method. Here, we provide
theoretical complexity results for a fixed stepsize version of the method and
report extensive numerical comparisons on both convex and nonconvex problems
demonstrating the efficiency of our approach.
