  We propose a new asynchronous parallel block-descent algorithmic framework
for the minimization of the sum of a smooth nonconvex function and a nonsmooth
convex one, subject to both convex and nonconvex constraints. The proposed
framework 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
current state-of-the-art models. Other key features of the framework are: i) it
covers in a unified way several specific solution methods; ii) it accommodates
a variety of possible parallel computing architectures; and iii) it can deal
with nonconvex constraints. Almost sure convergence to stationary solutions is
proved, and theoretical complexity results are provided, showing nearly ideal
linear speedup when the number of workers is not too large.
