An inexact interior point proximal method for the variational inequality problem (Q1020996)

An inexact interior point proximal method is developed for solving variational inequality problems with maximal monotone operators and linear constraints. The generalized proximal methods used for solving this kind of constrained convex optimization problems make the assumption that the feasible region has nonempty interior. The ``extragradient algorithm'' developed in this work is also applicable for problems whose feasible region may have empty interior. A full convergence analysis of the algorithm is performed. A numerical implementation of the algorithm is not presented.