• EXPLICIT PROJECTION METHODS FOR VARIATIONAL INEQUALITIES

Abstract

We present two explicit methods for solving variational inequalities. Each iteration of the proposed methods consists of projection onto a halfplace containing the feasible set. Our projection is easy to calculate. Moreover, we find the step size through an Armijo-like search instead of defining them exogenously. Our methods are proved to be globally convergent under pseudomontonicity and continuity of the operator. No coerciveness, paramonotonicity or Lipschitz continuity assumption is imposed, thus we generalize some recent results in the literature.

Mathematics Subject Classification (2010): 90C25.90C30.

Key words: Variational inequalities, Pseudomontone operator, Explicit projection algorithm, Global convergence.