An infeasible interior proximal method for the variational inequality problem
Geci Da Silva | Burachik, Regina | Lopes, Jurandir
maximal monotone operators | outer approximation algorithm | interior point method | global convergence
In this paper, we propose an infeasible interior proximal method for solving variational inequality problems with maximal monotone operators and linear constraints. The interior proximal method proposed by Auslender, Teboulle and Ben-Tiba is a proximal method using a distance-like barrier function and it has a global convergence property under mild assumptions. However this method is applicable only to problems whose feasible region has nonempty interior. The algorithm proposed in this paper is applicable to problems whose feasible region may have empty interior. Moreover, a new kind of inexact scheme is used. We present a full convergence analysis for our algorithm.