An inexact proximal decomposition method for variational inequalities with separable structure

This paper presents an inexact proximal method for solving monotone variational inequality problems with a given separable structure. The proposed algorithm is natural extension of the Proximal Multiplier Algorithm Distances (PMAPD) by Sarmiento et al . [ Optimization 65 (2016) 501–537], which unified works Chen and Teboulle (PCPM method), Kyono Fukushima (NPCPMM) developed convex programs particular resulting combines recent distances theory introduced Auslender SIAM J. Optim 16 (2006) 697–725] decomposition extends results Entropic Decomposition Method Teboulle, used to Logarithmic Quadratic distances. Under some mild assumptions on problem we prove global convergence primal–dual sequences produced algorithm.