A Strongly Convergent Modified Halpern Subgradient Extragradient Method for Solving the Split Variational Inequality Problem

We propose a method for solving the split variational inequality problem (SVIP) involving Lipschitz continuous and pseudomonotone mappings. The proposed method is inspired by the Halpern subgradient extragradient method for solving the monotone variational inequality problem with a simple step size. A strong convergence theorem for an algorithm for solving such a SVIP is proved without the knowledge of the Lipschitz constants of the mappings. As a consequence, we get a strongly convergent algorithm for finding the solution of the split feasibility problem (SFP), which requires only two projections at each iteration step. A simple numerical example is given to illustrate the proposed algorithm.