A Twice Extrapolated Algorithm for Solving Non-Lipschitz Bilevel Split Monotone Variational Inclusion Problem

In this paper, we introduce an efficient algorithm for solving bilevel split variational monotone inclusion problems. The class of problems studied in this paper contains several other classes of well-known problems which have been studied by many authors. Unlike several existing methods in the literature, our method does not require the underlying operators in the lower-level problem and upper-level to be Lipschitz continuous. The proposed method is a combination of the Tseng method and the projection and contraction method. The convergence of our new algorithm is enhanced with double inertial steps. We obtain the strong convergence results of our algorithm under mild conditions on the control parameters of our method. Furthermore, we carry out some numerical tests to show the advantage of our new method over many well-known methods. Our results improve, generalize, and unify several existing results in the literature.