  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.
