Accelerated Symmetric ADMM and Its Applications in Large-Scale Signal Processing (Journal of Computational Mathematics, 2024)
The alternating direction method of multipliers (ADMM) has been extensively investigated in the past decades for solving separable convex optimization problems, and surprisingly, it also performs efficiently for nonconvex programs. In this paper, we proposea symmetric ADMM based on acceleration techniques for a family of potentially nonsmoothand nonconvex programming problems with equality constraints, where the dual variablesare updated twice with different stepsizes. Under proper assumptions instead of the so-called Kurdyka-Lojasiewicz inequality, convergence of the proposed algorithm as well asits pointwise iteration-complexity are analyzed in terms of the corresponding augmentedLagrangian function and the primal-dual residuals, respectively. Performance of our algorithm is verified by numerical examples corresponding to signal processing applications insparse nonconvex/convex regularized minimization.
Keywords: Nonconvex optimization; Symmetric ADMM; Acceleration technique; Complexity; Signal processing.