Accelerated Hybrid Subgradient Extragradient Methods for Solving Bilevel Split Quasimonotone Variational Inequality Problems

In this paper, we introduce and study a modified inertial subgradient extragradient iterative algorithm for solving bilevel split quasimonotone variational inequality problems with a fixed point constraint of demimetric mappings in the framework of real Hilbert spaces. The method involves a strongly monotone operator at the upper-level problem and quasimonotone mapping at the lower level. We obtain a strong convergence result of the proposed method under some mild conditions on the algorithm parameters without the prior knowledge of the operator norm or the coefficient of the underlying operator in the scope of infinite dimensional real Hilbert spaces. Finally, some numerical demonstrations are given to illustrate the gains of this method. Our results generalize and improve some well-known results in the literature.