Finite-Value Superiorization for Variational Inequality Problems
  The main goal of this paper is to present the application of a superiorization methodology to solution of variational inequalities. Within this framework a variational inequality operator is considered as a small perturbation of a convex feasibility solver what allows to construct a simple iteration algorithm. The specific features of variational inequality problems allow to use a finite-value perturbation which may be advantageous from computational point of view. The price for simplicity and finite-value is that the algorithm provides an approximate solution of variational inequality problem with a prescribed coordinate accuracy. 
Evgeni Nurminski
math.OC