An efficient algorithm for updating the penalty parameter of the alternating direction method for l1 problem

Abstract

This work investigates an adaptively updating rule of the penalty in alternating direction method (ADM) for 𝑙 1 problem. The adjusting criterion is motivated by the iterative behaviors of the objective and residue of constraint. The main algorithm is focused on the ADM framework of the dual problem. By studying the iterative behaviors, the dynamically updating scheme is developed with default values of startup, frequency and scaling. Numerical experiments show that the novel algorithm can not only speed up the classic ADM, but also make the choice of initial penalty parameter more flexible.