Modified Extragradient Method for Variational Inequalities and Verification of Solution Existence.

In this paper, we propose a modified extragradient method for solving variational inequalities (VI) which has the following nice features: (i) The generated sequence possesses an expansion property with respect to the starting point; (ii) the existence of the solution to a VI problem can be verified through the behavior of the generated sequence from the fact that the iterative sequence diverges to infinity if and only if the solution set is empty. Global convergence of the method is guaranteed under mild conditions. Our preliminary computational experience is also reported. Key Words. Variational inequalities; projection-type methods; solution existence. [ABSTRACT FROM AUTHOR]