The primal Douglas-Rachford splitting algorithm for a class of monotone mappings with application to the traffic equilibrium problem

The paper applies the Douglas-Rachford splitting algotithm to a class of multi-valued equations consisting of the sum of two monotone mappings. Compared with the dual application of the same algorithm, which is known as the alternating direction method for multipliers, the primal application yields algorithms that seem somewhat involved. However, the resulting algorithms may be applied effectively to problems with certain special structure. In particular the paper shows that they can be used to derive decomposition algorithms for solving the variational inequality formulation of the traffic equilibrium problem.