Parallel and distributed methods for nonconvex optimization

Abstract

We propose a general algorithmic framework for the minimization of a nonconvex smooth function subject to nonconvex smooth constraints. The algorithm solves a sequence of (separable) strongly convex problems. Convergence to a stationary solution of the original nonconvex optimization is established. Our framework is very general and flexible; it unifies several existing Successive Convex Approximation (SCA)-based algorithms such as (proximal) gradient or Newton type methods, block coordinate (parallel) descent schemes, difference of convex functions methods, and improves on their convergence properties. More importantly, and differently from current SCA schemes, it naturally leads to distributed and parallelizable schemes for a large class of nonconvex problems. The new method is applied to the solution of a new rate profile optimization problem over Interference Broadcast Channels (IBCs); numerical results show that it outperforms existing ad-hoc algorithms.