A customized Douglas–Rachford splitting algorithm for separable convex minimization with linear constraints

We consider applying the Douglas–Rachford splitting method (DRSM) to the convex minimization problem with linear constraints and a separable objective function. The dual application of DRSM has been well studied in the literature, resulting in the well known alternating direction method of multipliers (ADMM). In this paper, we show that the primal application of DRSM in combination with an appropriate decomposition can yield an efficient structure-exploiting algorithm for the model under consideration, whose subproblems could be easier than those of ADMM. Both the exact and inexact versions of this customized DRSM are studied; and their numerical efficiency is demonstrated by some preliminary numerical results.