In this paper we introduce an inexact proximal point algorithm using proximal distances for solving variational inequality problems when the mapping is pseudomonotone or quasimonotone. Under some natural assumptions we prove that the sequence generates by the algorithm is convergent for the pseudomonotone case and weakly convergent for the quasimonotone ones. This approach unifies the results obtained by Auslender, Teboulle and Ben-Tiba (1999), Brito et al. (2012) and extends the convergence properties for the class of divergence distances and Bregman distances.
View An Inexact Proximal Algorithm for Pseudomonotone and Quasimonotone Variational Inequalities