An efficient iterative method for solving quasimonotone bilevel split variational inequality problem

Abstract

In this paper, we introduce and study a modified inertial subgradient extragradient iterative method for solving bilevel split quasimonotone variational inequality problems in the framework of real Hilbert spaces. The method involves strongly monotone operators and quasimonotone operators as the cost operators. In addition, we obtain a strong convergence result of the proposed method under some standard conditions on the control parameters of the method. Our method does not require the prior knowledge of the operator norm or the coefficient of the underlying operator in the space of infinite dimensional real Hilbert spaces. Finally, we provide some numerical experiments to demonstrate the efficiency of our proposed methods in comparison with some existing methods. Our result generalizes and improves some well-known results in literature.