An extragradient algorithm for solving bilevel pseudomonotone variational inequalities (Q427380)

Variational inequalities are usually solved by projection methods. It is known that the projection methods will not converge when the cost operator is monotone. Extragradient methods have been proposed to overcome this drawback. Extragradient methods were extended for solving pseudo-monotone variational inequalities and equilibrium problems using Tikhonov regularization. However they require some monotonicity properties. The authors propose an extragradient method to solve bilevel pseudo-monotone variational inequalities without regularization. It is shown that the algorithm converges under mild conditions.