An Efficient Projection Method for Generalized Variational Inequalities Problem

Abstract

In this paper, we propose a new version of a projection algorithm for the generalized variational inequalities problem (GVIP) involving a multi-valued mapping. In this work, we introduce a new combination of the main algorithmic steps proposed in projection methods that have been developed previously for classical or generalized variational inequalities problem with the aim of significantly reducing the computational cost. For the convergence, the assumptions required for the underlying mapping are continuity and a condition that is weaker than the pseudo-monotonicity. We show that this method is well-defined and its corresponding algorithm is globally convergent. Preliminary comparative experiments on several test problems to validate the effectiveness of the proposed method.