Conditional extragradient algorithms for solving variational   inequalities
  In this paper, we generalize the classical extragradient algorithm for solving variational inequality problems by utilizing nonzero normal vectors of the feasible set. In particular, conceptual algorithms are proposed with two different linesearchs. We then establish convergence results for these algorithms under mild assumptions. Our study suggests that nonzero normal vectors may significantly improve convergence if chosen appropriately. 
J.Y. Bello Cruz, R. D\'iaz Mill\'an, Hung M. Phan
math.OC