EFFICIENT EXTRAGRADIENT METHODS FOR BILEVEL PSEUDOMONOTONE VARIATIONAL INEQUALITIES WITH NON-LIPSCHITZ OPERATORS AND THEIR APPLICATIONS.

In this paper, four extragradient-type algorithms are presented for solving bilevel variational inequalities of pseudomonotone and non-Lipschitz continuous operators in real Hilbert spaces. The proposed iterative schemes employ two Armijo-type linesearch methods making them work adaptively. Strong convergence theorems of the suggested algorithms are established under some mild conditions. Finally, some numerical experiments and applications are given to verify the advantages and efficiency of the proposed algorithms over some previously known ones. [ABSTRACT FROM AUTHOR]