A Novel approach for the solvability of Monotone Bilevel framework for split variational inequality problems within Hilbert setting optimization

This paper presents a novel algorithm modified inertial Tseng extragradient approach with a self-adaptive step size for the approximation of the solutions for the celebrated bilevel split variational inequality problem in the framework of Hilbert setting. Using the approach of projections onto a constructible half-space, we establish the required strong convergence result for the proposed iterative technique. Our method does not require prior techniques of the Lipschitz type constant for the cost operators. Finally, we present several numerical experi- ments that show how much efficient and applicable the proposed techniques are in contrast with the well-known existing results. MSC Classification: 47H06 , 47H09 , 47J05 , 47J25