A self adaptive method for solving a class of bilevel variational inequalities with split variational inequality and composed fixed point problem constraints in Hilbert spaces.
In this paper, the authors propose an inertial extrapolation method for solving a class of bilevel variational inequalities. This involves a split variational inequality and a composed fixed point problem in real Hilbert spaces. The strong convergence results of this method are proved under the assumptions of strong monotonicity and Lipschitz continuous pseudomonotonicity. Some numerical experiments are given to show the efficiency and applicability of this method in comparison with the algorithm in [N.~M. Hai, L.~H.~M. Van and T.~V. Anh, Acta Math. Vietnam. {\bf 46} (2021), no.~3, 515--530; MR4292209] in the framework of infinite-dimensional Hilbert spaces. It is worth mentioning that the proof of this method does not rely on the conventional two cases approach [see op. cit.; P.-É. Maingé, SIAM J. Control Optim. {\bf 47} (2008), no.~3, 1499--1515; MR2407025] for strong convergence. The results obtained in the work under review improve and extend several results in this direction.