An inertial proximal alternating direction method of multipliers for nonconvex optimization

Abstract

The alternating direction method of multipliers (ADMM) is an efficient method for solving separable problems. However, ADMM may not converge when there is a nonconvex function in the objective. The main contributions of this paper are proposing and analysing an inertial proximal ADMM for a class of nonconvex optimization problems. The proposed algorithm combines the basic ideas of the proximal ADMM and the inertial proximal point method. The global and strong convergence of the proposed algorithm is analysed under mild conditions. Finally, we give some preliminary numerical results to show the effectiveness of the proposed algorithm.