Accelerated Symmetric ADMM and Its Applications in Signal Processing

Abstract

The alternating direction method of multipliers (ADMM) were extensively investigated in the past decades for solving separable convex optimization problems. Fewer researchers focused on exploring its convergence properties for the nonconvex case although it performed surprisingly efficient. In this paper, we propose a symmetric ADMM based on different acceleration techniques for a family of potentially nonsmooth nonconvex programing problems with equality constraints, where the dual variables are updated twice with different stepsizes. Under proper assumptions instead of using the so-called Kurdyka-Lojasiewicz inequality, convergence of the proposed algorithm as well as its pointwise iteration-complexity are analyzed in terms of the corresponding augmented Lagrangian function and the primal-dual residuals, respectively. Performance of our algorithm is verified by some preliminary numerical examples on applications in sparse nonconvex/convex regularized minimization signal processing problems.

arXiv comment20 pages, submitted

References in corpus (4)

• Generalized Symmetric ADMM for Separable Convex Optimization
• Convergence rate bounds for a proximal ADMM with over-relaxation stepsize parameter for solving nonconvex linearly constrained problems
• A parameterized proximal point algorithm for separable convex optimization
• Linearized ADMM for Non-convex Non-smooth Optimization with Convergence Analysis

Cited by in corpus (1)

• A family of multi-parameterized proximal point algorithms