Modified Tseng’s extragradient methods for the minimum-norm solutions of the pseudo-monotone split variational inequality problems

In this paper, we propose two modified Tseng’s extragradient methods for the split variational inequality problem. When the mappings are Lipschitz continuous, we develop a modified Tseng’s extragradient method with a self-adaptive step size. For pseudo-monotone, sequentially weakly continuous, and Lipschitz continuous mappings, we prove that the sequence generated by this algorithm converges strongly to the minimum-norm solution. When the mappings are uniformly continuous, we introduce a modified Tseng’s extragradient method with line search. For pseudo-monotone, sequentially weakly continuous, and uniformly continuous mappings, we prove its strong convergence to the minimum-norm solution. Finally, numerical experiments are presented to demonstrate the performance of the proposed methods.