A fixed point iteration algorithm is introduced to solve bilevel monotone variational inequalities. The algorithm uses simple projection sequences. Strong convergence of the iteration sequences generated by the algorithm to the solution is guaranteed under some assumptions in a real Hilbert space. MSC: 65K10; 90C25

In this paper, we present an interior approximal method for solving equilibrium problems for pseudomonotone bifunctions without Lipschitz-type continuity on polyhedra. The method can be viewed as combining a special interior proximal function, which replaces the usual quadratic function, Armijo-type linesearch techniques and the cutting hyperplane methods. Convergence properties of the method are established, among them the global convergences are proved under few assumptions. Finally, we present some preliminary computational results to Cournot-Nash oligopolistic market equilibrium models. MSC: 65K10; 90C25