  Communication delays and synchronization are major bottlenecks for parallel
computing, and tolerating asynchrony is therefore crucial for accelerating
parallel computation. Motivated by optimization problems that do not satisfy
convexity assumptions, we present an asynchronous block coordinate descent
algorithm for nonconvex optimization problems whose objective functions satisfy
the Polyak-Lojasiewicz condition. This condition is a generalization of strong
convexity to nonconvex problems and requires neither convexity nor uniqueness
of minimizers. Under only assumptions of mild smoothness of objective functions
and bounded delays, we prove that a linear convergence rate is obtained.
Numerical experiments for logistic regression problems are presented to
illustrate the impact of asynchrony upon convergence.
