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In this paper, we propose modified Tseng's extragradient methods with self-adaptive step size for solving a bilevel split variational inequality problem (BSVIP) involving a strongly monotone mapping in the upper-level problem and pseudomonotone mappings in the lower-level one. This algorithm is very simple in the sense that it requires only two projections at each iteration step. The strong convergence of the proposed algorithm is established without the prior knowledge of the Lipschitz and strongly monotone constants of the mappings. In addition, the implementation of the method does not require the computation or estimation of the norm of the given operator, which is in general not an easy work in practice. Special cases are considered. Finally, a numerical example is given to illustrate the performance of the proposed algorithm in comparison with a previously known the subgradient extragradient algorithm.

Modified Tseng's extragradient methods with self-adaptive step size for solving bilevel split variational inequality problems