A Relaxed Inertial Tseng’s Extragradient Method for Solving Split Variational Inequalities with Multiple Output Sets

Recently, the split inverse problem has received great research attention due to its several applications in diverse fields. In this paper, we study a new class of problems called variational inequality with multiple output sets. We propose Tseng extragradient method, which uses self-adaptive step sizes for approximating solution when cost operators are pseudomonotone and non-Lipschitz framework Hilbert spaces. point out that while non-Lipschitz, our proposed method does not involve any linesearch procedure implementation. Instead, employ more efficient size technique known parameters. addition, relaxation inertial improve convergence properties algorithm. Moreover, under some mild conditions on control parameters without knowledge operators’ norm, prove sequence generated by converges strongly minimum-norm problem. Finally, apply result certain classes optimization problems, present numerical experiments demonstrate applicability method. Several existing results literature direction could be viewed as special cases study.