Accelerated ADMM based on Accelerated Douglas-Rachford Splitting

Abstract

Alternating direction method of multipliers (ADMM) is a form of augmented Lagrangian optimisation algorithm that found its place in many new applications in recent years. This paper explores a possibility for an upgrade of the ADMM by extrapolation-based acceleration, which has been successfully utilised for a long time in case of accelerated gradient method. The development uses a recently proposed accelerated Duglas-Rachford splitting by applying it on Fenchel dual problem, resulting in a method that replaces the classical proximal point convergence mechanism of ADMM with the accelerated gradient. The obtained method requires that the second function involved in the cost is strongly convex quadratic, as well as an upper bound on the penalty parameter. A heuristic modification of the derived method is described, and numerical experiments are performed by solving a randomly generated quadratic programming (QP) problem.