A Viscosity-Type Tseng'S Extragradient Algorithm for Bilevel Split Hierarchical Variational Inequalities With Multiple Output Sets

In this paper, we introduce and study a new class of split inverse problems called bilevel split hierarchical variational inequality problem with multiple output sets in the framework of real Hilbert spaces. We propose a viscosity-type Tseng's extragradient method for solving this problem when the cost operators are pseudomonotone. Under mild conditions, we obtain a strong convergence result for the proposed algorithm. Finally, we present numerical experiments to illustrate the applicability of our method.