Anderson Accelerated Operator Splitting Methods for Convex-Nonconvex Regularized Problems

Abstract

Convex–nonconvex (CNC) regularization is a novel paradigm that employs a nonconvex penalty function while preserving the convexity of the overall objective function. It has found successful applications in signal processing, statistics, and machine learning. Despite its wide applicability, the computation of CNC-regularized problems is still dominated by the forward–backward splitting method, which can be computationally slow in practice and is restricted to handling a single regularizer. To address these limitations, we develop a unified Anderson acceleration framework that encompasses multiple prevalent operator-splitting schemes, thereby enabling the efficient solution of a broad class of CNC-regularized problems with a quadratic data-fidelity term. We establish global convergence of the proposed algorithm to an optimal point and demonstrate its substantial speed-ups across diverse applications.