Inertial self-adaptive algorithms for solving non-Lipschitz monotone variational inclusion problems

Abstract In this paper, we introduce a modified Tseng extragradient for solving monotone variational inclusion problem in real Hilbert spaces. Our method does not require the associated single-valued operator to be Lipschitz continuous. Rather, it requires uniform continuity which is a weaker assumption. We prove the strong convergence of our new method under some condition on the control parameter. We carry out numerical experiment to show the computational advantage of the new method over some existing methods in the literature. Our results extends and generalizes some well known results in literature.