On the equivalence of the primal-dual hybrid gradient method and Douglas–Rachford splitting

Abstract

The primal-dual hybrid gradient (PDHG) algorithm proposed by Esser, Zhang, and Chan, and by Pock, Cremers, Bischof, and Chambolle is known to include as a special case the Douglas–Rachford splitting algorithm for minimizing the sum of two convex functions. We show that, conversely, the PDHG algorithm can be viewed as a special case of the Douglas–Rachford splitting algorithm.