Scalable nonconvex inexact proximal splitting

We study a class of large-scale, nonsmooth, and nonconvex optimization problems. In particular, we focus on nonconvex problems with composite objectives. This class includes the extensively studied class of convex composite objective problems as a subclass. To solve composite nonconvex problems we introduce a powerful new framework based on asymptotically nonvanishing errors, avoiding the common stronger assumption of vanishing errors. Within our new framework we derive both batch and incremental proximal splitting algorithms. To our knowledge, our work is first to develop and analyze incremental nonconvex proximal-splitting algorithms, even if we were to disregard the ability to handle nonvanishing errors. We illustrate one instance of our general framework by showing an application to large-scale nonsmooth matrix factorization.